U.S. patent application number 13/378028 was filed with the patent office on 2012-04-12 for synchronized express and local trains for urban commuter rail systems.
This patent application is currently assigned to INTEGRATED TRANSPORTATION TECHNOLOGIES, L.L.C.. Invention is credited to Joong H. Chun.
Application Number | 20120085871 13/378028 |
Document ID | / |
Family ID | 43899118 |
Filed Date | 2012-04-12 |
United States Patent
Application |
20120085871 |
Kind Code |
A1 |
Chun; Joong H. |
April 12, 2012 |
Synchronized Express And Local Trains For Urban Commuter Rail
Systems
Abstract
A computerized system and method of managing subway trains along
a two-track subway line to allow express travel in combination with
local service. Express trains catch up to local trains at express
stations along the line, and provision is made to allow the express
trains to physically or "virtually" pass the local train at those
stations. Embodiments in which the express trains physically pass
the local train include direct train-to-train transfer facilitated
by side-by-side tracks at the express station occupying reduced
foot-print. In other embodiments, virtual passing is accomplished
by changing the type of service provided by trains at express
intervals: a local train "transforms" into an express train and
vice versa. Embodiments enable passengers to transfer between
trains at express stations so that these "relay" passengers can
travel faster than any specific train.
Inventors: |
Chun; Joong H.; (Plano,
TX) |
Assignee: |
INTEGRATED TRANSPORTATION
TECHNOLOGIES, L.L.C.
Plano
TX
|
Family ID: |
43899118 |
Appl. No.: |
13/378028 |
Filed: |
October 19, 2010 |
PCT Filed: |
October 19, 2010 |
PCT NO: |
PCT/US2010/053237 |
371 Date: |
December 13, 2011 |
Current U.S.
Class: |
246/2S ;
701/19 |
Current CPC
Class: |
B61B 1/00 20130101; B61L
27/0016 20130101; B61L 27/0027 20130101 |
Class at
Publication: |
246/2.S ;
701/19 |
International
Class: |
B61L 27/00 20060101
B61L027/00; B61B 1/02 20060101 B61B001/02; B61L 27/04 20060101
B61L027/04; B61B 1/00 20060101 B61B001/00 |
Foreign Application Data
Date |
Code |
Application Number |
Oct 23, 2009 |
US |
12604490 |
Claims
1-6. (canceled)
7. A method of operating a subway line having a single track in a
direction of travel, comprising the steps of: operating a local
train to travel along the track from a first express station toward
a second express station; operating an express train to travel
along the single track behind the local train, the express train
leaving the first express station later than the local train but
traveling at a faster travel velocity to arrive at the second
express station at or near the time that the local train is at the
second express station; and passing the local train with the
express train at the second express station; wherein the second
express station includes a passenger platform; wherein the step of
operating the local train comprises: operating a first train to
travel along the single track from the first express station,
stopping for passenger transfer at least one time at a local
station along the subway line between the first and second express
stations; wherein the step of operating the express train
comprises: operating a second train to travel along the single
track without stopping at the local station, the second train
leaving the first express station later than the first train but
traveling at a faster travel velocity; wherein the passing step
comprises: stopping the first train at the second express station
to allow passengers to board and de-board the first train from and
to the passenger platform; then operating the first train to
proceed along the single track from the second express station as
an express train; then stopping the second train at the second
express station to allow passengers to board and de-board the
second train from and to the passenger platform; and then operating
the second train to proceed along the single track from the second
express station as a local train, the second train stopping for
passenger transfer at least one time at a local station along the
subway line after the second express station; and wherein the step
of operating the first train as an express train comprises
operating the first train to travel without stopping at the local
station after the second express station.
8. The method of claim 7, wherein the step of operating the express
train further comprises: operating a third train to travel along
the single track without stopping at the local station, the third
train leaving the first express station later than the first train
but traveling at a faster travel velocity, and leaving the first
express station earlier than the second train; and and wherein the
passing step further comprises: after the step of operating the
first train to proceed along the single track from the second
express station as an express train, and before the step of
stopping the second train at the second express station: stopping
the third train at the second express station to allow passengers
to board and de-board the third train from and to the passenger
platform; and then operating the third train to proceed along the
single track from the second express station as an express
train.
9. The method of claim 8, wherein the step of operating the express
train further comprises: stopping the third train along the single
track between the first and second express stations at a local
station at which the second train does not stop but at which the
first train stops.
10. The method of claim 8, further comprising: operating a fourth
train to travel along the single track without stopping at the
local station, the fourth train leaving the first express station
later than the first train but traveling at a faster travel
velocity, and leaving the first express station earlier than the
second train; and after the step of operating the first train to
proceed along the single track from the second express station as
an express train, and before the step of stopping the second train
at the second express station: stopping the fourth train at the
second express station to allow passengers to board and de-board
the fourth train from and to the passenger platform; and then
operating the fourth train to proceed along the single track from
the second express station as an express train.
11. The method of claim 7, wherein the step of stopping the second
train at the express station occurs after only a brief time after
the step of operating the first train to proceed along the single
track from the second express station begins.
12. The method of claim 7, further comprising: before the step of
stopping the first train at the second express station to allow
passengers to board and de-board the first train from and to the
passenger platform, stopping the first train at the second express
station so that at least a portion of the passenger platform is not
aligned with the passenger platform; then stopping the second train
at the second express station so that a front portion of the first
train aligns with a portion of the passenger platform at the second
express station, to allow passengers to de-board the second train
to the passenger platform; wherein the step of stopping the first
train at the second express station to allow passengers to board
and de-board the first train from and to the passenger platform is
performed after passengers have de-boarded the second train to the
passenger platform; and further comprising: then stopping the
second train at the second express station to allow passengers to
board and de-board the second train from and to the passenger
platform.
13. The method of claim 7, wherein the step of operating the
express train further comprises: operating a third train to travel
along the single track without stopping at the local station, the
third train leaving the first express station later than the first
train but traveling at a faster travel velocity, and leaving the
first express station earlier than the second train; before the
step of stopping the first train at the second express station to
allow passengers to board and de-board the first train from and to
the passenger platform, stopping the second and third trains at the
second express station so that a front portion of the third train
aligns with a portion of the passenger platform at the second
express station, to allow passengers to de-board the third train to
the passenger platform; wherein the step of stopping the first
train at the second express station to allow passengers to board
and de-board the first train from and to the passenger platform is
performed after passengers have de-boarded the third train to the
passenger platform; and further comprising: then stopping the third
train at the second express station to allow passengers to board
and de-board the third train from and to the passenger
platform.
14. The method of claim 7, further comprising: operating a third
train to travel along the single track without stopping at the
local station, the third train leaving the first express station
later than the first train but traveling at a faster travel
velocity, and leaving the first express station earlier than the
second train; operating a fourth train to travel along the single
track without stopping at the local station, the fourth train
leaving the first express station later than the first train but
traveling at a faster travel velocity, and leaving the first
express station earlier than the second train; before the step of
stopping the first train at the second express station to allow
passengers to board and de-board the first train from and to the
passenger platform, stopping the third and fourth trains at the
second express station so that a front portion of the fourth train
aligns with a portion of the passenger platform at the second
express station, to allow passengers to de-board the fourth train
to the passenger platform; wherein the step of stopping the first
train at the second express station to allow passengers to board
and de-board the first train from and to the passenger platform is
performed after passengers have de-boarded the fourth train to the
passenger platform; and further comprising: then stopping the
fourth train at the second express station to allow passengers to
board and de-board the fourth train from and to the passenger
platform.
15. (canceled)
16. A method of operating a computer system to manage the
scheduling and operating of a subway line having a single track in
a direction of travel, comprising the steps of: retrieving, from a
memory resource, data representative of passenger usage of the
subway line; retrieving, from a memory resource, data
representative of train resources and properties associated with
the subway line; retrieving, from a memory resource, data
representative of the locations and properties of stations along
the subway line; from the retrieved data, deriving a schedule of
local and express trains operating along the subway line, relative
to local and express stations along the subway line, in at least
one direction of travel, so that trains operating as express trains
catch up to local trains leading the express trains along the
subway line only at express stations; wherein the derived schedule
is based on express trains passing local trains at the express
stations; and wherein the data representative of properties of
stations along the subway line comprises data representative of
which stations are express stations and which stations are local
stations.
17-19. (canceled)
20. A method of operating a computer system to manage the
scheduling and operating of a subway line having a single track in
a direction of travel, comprising the steps of: retrieving, from a
memory resource, data representative of passenger usage of the
subway line; retrieving, from a memory resource, data
representative of train resources and properties associated with
the subway line; retrieving, from a memory resource, data
representative of the locations and properties of stations along
the subway line; from the retrieved data, deriving a schedule of
local and express trains operating along the subway line, relative
to local and express stations along the subway line, in at least
one direction of travel, so that trains operating as express trains
catch up to local trains leading the express trains along the
subway line only at express stations; wherein the derived schedule
is based on express trains passing local trains at the express
stations; and wherein the step of deriving the schedule comprises:
also deriving car assignments corresponding to time of day and to
origin and destination stations for a passenger trip.
21. The method of claim 20, further comprising: communicating the
derived schedule and car assignments to passengers.
22. The method of claim 21, wherein the communicating step is
performed by way of one or more of a group consisting of video
displays at stations, video displays on trains, and information
communicated along with purchased tickets.
23. The method of claim 21, wherein the derived schedule and car
assignments communicated to passengers also comprises:
identification of stations at which a passenger may transfer
forward to a train ahead of the train the passenger is currently
riding on.
24. A method of operating a computer system to manage the
scheduling and operating of a subway line having a single track in
a direction of travel, comprising the steps of: retrieving, from a
memory resource, data representative of passenger usage of the
subway line; retrieving, from a memory resource, data
representative of train resources and properties associated with
the subway line; retrieving, from a memory resource, data
representative of the locations and properties of stations along
the subway line; from the retrieved data, deriving a schedule of
local and express trains operating along the subway line, relative
to local and express stations along the subway line, in at least
one direction of travel, so that trains operating as express trains
catch up to local trains leading the express trains along the
subway line only at express stations; wherein the derived schedule
is based on express trains passing local trains at the express
stations; wherein the deriving step derives a rush-hour schedule,
in which a first plurality of stations along the subway line are
identified as express stations; and further comprising: from the
retrieved data, deriving a non-rush hour schedule of local and
express trains operating along the subway line, relative to local
and express stations along the subway line, in at least one
direction of travel, so that trains operating as express trains
catch up to local trains leading the express trains along the
subway line only at express stations; wherein the derived schedule
is based on express trains passing local trains at the express
stations; and wherein the step of deriving the non-rush hour
schedule identifies a second plurality of stations along the subway
line as express stations, the second plurality of stations being a
subset of the first plurality of stations.
25. (canceled)
26. A computer-readable medium storing a computer program that,
when executed on a computer system, causes the computer system to
perform a pluralitperations for manain the scheduling and operation
of a subway having a single track in a direction of travel, the
plurality of operations comprising: retrieving, from a memory
resource in the computer system, data representative of passenger
usage of the subway line; retrieving, from a memory resource in the
computer system, data representative of train resources and
properties associated with the subway line; retrieving, from a
memory resource in the computer system, data representative of the
locations and properties of stations along the subway line; from
the retrieved data, deriving a schedule of local and express trains
operating along the subway line, relative to local and express
stations along the subway line, in at least one direction of
travel, so that trains operating as express trains catch up to
local trains leading the express trains along the subway line only
at express stations; wherein the derived schedule is based on
express trains passing local trains at the express stations; and
wherein the data representative of properties of stations along the
subway line comprises data representative of which stations are
express stations and which stations are local stations.
27-29. (canceled)
30. A computer-readable medium storing a computer program that,
when executed on a computer system, causes the computer system to
perform a plurality of operations for managing the scheduling and
operation of a subway line having a single track in a direction of
travel, the plurality of operations comprising: retrieving, from a
memory resource in the computer system, data representative of
passenger usage of the subway line; retrieving, from a memory
resource in the computer system, data representative of train
resources and properties associated with the subway line;
retrieving, from a memory resource in the computer system, data
representative of the locations and properties of stations along
the subway line; from the retrieved data, deriving a schedule of
local and express trains operating along the subway line, relative
to local and express stations along the subway line, in at least
one direction of travel, so that trains operating as express trains
catch up to local trains leading the express trains along the
subway line only at express stations; wherein the derived schedule
is based on express trains passing local trains at the express
stations; and wherein the operation of deriving the schedule
comprises: also deriving car assignments corresponding to time of
day and to origin and destination stations for a passenger
trip.
31. The computer-readable medium of claim 30, wherein the plurality
of operations further comprises: communicating the derived schedule
and car assignments to passengers.
32. The computer-readable medium of claim 31, wherein the
communicating operation is performed by way of one or more of a
group consisting of video displays at stations, video displays on
trains, and information communicated along with purchased
tickets.
33. The computer-readable medium of claim 31, wherein the derived
schedule and car assignments communicated to passengers also
comprises: identification of stations at which a passenger may
transfer forward to a train ahead of the train the passenger is
currently riding on.
34. A computer-readable medium storing a computer program that,
when executed on a computer system, causes the computers system to
perform a plurality operations for managing the scheduling and
operation of a subway line having a single track in a direction of
travel, the plurality of operations comprising: retrieving, from a
memory resource in the computer system, data representative of
passenger usage of the subway line; retrieving, from a memory
resource in the computer system, data representative of train
resources and properties associated with the subway line;
retrieving, from a memory resource in the computer system, data
representative of the locations and properties of stations along
the subway line; from the retrieved data, deriving a schedule of
local and express trains operating along the subway line, relative
to local and express stations along the subway line, in at least
one direction of travel, so that trains operating as express trains
catch up to local trains leading the express trains along the
subway line only at express stations; wherein the derived schedule
is based on express trains passing local trains at the express
stations; wherein the deriving operation derives a rush-hour
schedule, in which a first plurality of stations along the subway
line are identified as express stations; and wherein the plurality
of operations further comprises: from the retrieved data, deriving
a non-rush hour schedule of local and express trains operating
along the subway line, relative to local and express stations along
the subway line, in at least one direction of travel, so that
trains operating as express trains catch up to local trains leading
the express trains along the subway line only at express stations;
wherein the derived schedule is based on express trains passing
local trains at the express stations; and wherein the operation of
deriving the non-rush hour schedule identifies a second plurality
of stations along the subway line as express stations, the second
plurality of stations being a subset of the first plurality of
stations.
35. (canceled)
36. A computer system for managing the scheduling and operation of
a subway line having a single track in a direction of travel,
comprising: an input device for receiving inputs from a user of the
system; at least one memory resource for storing data, the data
including data representative of inputs from the user of the
system; one or more central processing units coupled to the input
device, for executing program instructions; and program memory,
coupled to the one or more central processing units, for storing a
computer program including program instructions that, when executed
by the one or more central processing units, cause the computer
system to perform a plurality of operations for managing the
scheduling and operation of a subway line having a single track in
a direction of travel, the plurality of operations comprising:
retrieving, from a memory resource, data representative of
passenger usage of the subway line; retrieving, from a memory
resource, data representative of train resources and properties
associated with the subway line; retrieving, from a memory
resource, data representative of the locations and properties of
stations along the subway line; from the retrieved data, deriving a
schedule of local and express trains operating along the subway
line, relative to local and express stations along the subway line,
in at least one direction of travel, so that trains operating as
express trains catch up to local trains leading the express trains
along the subway line only at express stations; wherein the derived
schedule is based on express trains passing local trains at the
express stations; and wherein the data representative of properties
of stations along the subway line comprises data representative of
which stations are express stations and which stations are local
stations.
37-39. (canceled)
40. A computer system for managing the scheduling and operation of
a subway line having a single track in a direction of travel,
comprising: an input device for receiving inputs from a user of the
system; at least one memory resource for storing data, the data
including data representative of inputs from the user of the
system; one or more central processing units coupled to the input
device, for executing program instructions; and program memory,
coupled to the one or more central processing units, for storing a
computer program including program instructions that, when executed
by the one or more central processing units, cause the computer
system to perform a plurality of operations for the scheduling and
operation of a subway line having a single track in a direction of
travel, the plurality of operations comprising: retrieving, from a
memory resource, data representative of passenger usage of the
subway line; retrieving, from a memory resource, data
representative of train resources and properties associated with
the subway line; retrieving, from a memory resource, data
representative of the locations and properties of stations along
the subway line; from the retrieved data, deriving a schedule of
local and express trains operating along the subway line, relative
to local and express stations along the subway line, in at least
one direction of travel, so that trains operating as express trains
catch up to local trains leading the express trains along the
subway line only at express stations; wherein the derived schedule
is based on express trains passing local trains at the express
stations; wherein the operation of deriving the schedule comprises:
also deriving car assignments corresponding to time of day and to
origin and destination stations for a passenger trip.
41. The system of claim 40, wherein the plurality of operations
further comprises: communicating the derived schedule and car
assignments to passengers.
42. The system of claim 41, further comprising: at least one output
device, coupled to the one or more central processing units,
comprising one or more of a group consisting of video displays at
stations, video displays on trains, and information communicated
along with purchased tickets; wherein the communicating operation
is performed by way of the at least one output device.
43. The system of claim 41, wherein the derived schedule and car
assignments communicated to passengers also comprises:
identification of stations at which a passenger may transfer
forward to a train ahead of the train the passenger is currently
riding on.
44. A computer system for managing the scheduling and operation of
a subway line having a single track in a direction of travel,
comprising: an input device for receiving inputs from a user of the
system; at least one memory resource for storing data, the data
including data representative of inputs from the user of the
system; one or more central processing units coupled to the input
device, for executing program instructions; and program memory,
coupled to the one or more central processing units, for storing a
computer program including program instructions that, when executed
by the one or more central processing units, cause the computer
system to perform a plurality of operations for managing the
scheduling and operation of a subway line having a single track in
a direction of travel, the plurality of operations comprising:
retrieving, from a memory resource, data representative of
passenger usage of the subway line; retrieving, from a memory
resource, data representative of train resources and properties
associated with the subway line; retrieving, from a memory
resource, data representative of the locations and properties of
stations along the subway line; from the retrieved data, deriving a
schedule of local and express trains operating along the subway
line, relative to local and express stations along the subway line,
in at least one direction of travel, so that trains operating as
express trains catch up to local trains leading the express trains
along the subway line only at express stations; wherein the derived
schedule is based on express trains passing local trains at the
express stations; wherein the deriving operation derives a
rush-hour schedule, in which a first plurality of stations along
the subway line are identified as express stations; and wherein the
plurality of operations further comprises: from the retrieved data,
deriving a non-rush hour schedule of local and express trains
operating along the subway line, relative to local and express
stations along the subway line, in at least one direction of
travel, so that trains operating as express trains catch up to
local trains leading the express trains along the subway line only
at express stations; wherein the derived schedule is based on
express trains passing local trains at the express stations; and
wherein the operation of deriving the non-rush hour schedule
identifies a second plurality of stations along the subway line as
express stations, the second plurality of stations being a subset
of the first plurality of stations.
Description
BACKGROUND OF THE INVENTION
[0001] This invention is in the field of mass transit systems.
Embodiments of this invention are more specifically directed to
scheduling and operation of mass transit commuter rail systems.
[0002] For many years, citizens of major metropolitan areas
throughout the world have relied on commuter rail systems,
including surface rail and subways, as an important means of
transportation. Because at-grade intersections with motor vehicles
are avoided by subway trains, subway systems are especially
attractive in densely populated cities. Currently, over one hundred
cities in the world operate subway commuter rail systems, serving
hundreds of millions of passengers each day.
[0003] Commuter rail systems in general, and subway systems in
particular, are of course constrained to the physical locations of
their tracks and stations. Trains cannot travel except along the
rails, and do not stop for loading and unloading except at discrete
stations along the railway. The construction cost of the
infrastructure components of railways, rails, and stations is a
primary determination in the overall size and complexity of a
subway system, especially considering the excavation required to
build a subway line within (and thus under) an existing city.
Because of these constraints, and of the cost required to add lines
or additional infrastructure, optimal utilization of the
transportation capacity provided by the subway commuter rail system
is a highly desirable goal. Underutilization of the subway system
is a financial disaster, in that the huge infrastructure costs are
not recouped; as such, subway commuter rail construction is often
confined to routes that are capable of providing adequate
ridership. But these infrastructure costs also inhibit additional
capacity from being constructed, if demand for the subway system
exceeds its capacity. As a result, many of the world's urban subway
systems are overcrowded; indeed, the overcrowded subway systems in
Seoul, Korea and Tokyo, Japan often receive worldwide publicity. My
U.S. Pat. No. 5,176,082, issued Jan. 5, 1993, describes a passenger
loading and unloading control system that provides one way of
addressing this overcrowding problem, specifically by scheduling
the number of passengers that may board individual train cars at a
station according to the number of passengers that are already on
those cars; a method of simultaneously loading and unloading
passengers, in an orderly manner, is also described in my
patent.
[0004] The constraint of high infrastructure construction costs is
also reflected in passenger travel times. Commuter rail systems
present the particular problem that passengers are free to board
and exit the subway train at any station along the line. For
example, a train that makes n stops along its line will have
.SIGMA..sub.j=2.sup.n(j-1) possible individual passenger trips,
with the particular trip made by a given passenger defined by the
station at which the passenger boards (i.e., the trip origin) and
the station at which the passenger chooses to exit the train (i.e.,
the destination). And, of course, ridership depends on the
convenience provided by the subway, which in large part depends on
the proximity of subway stations to passenger destinations. The
subway system designer and operator is thus faced with a tradeoff
between the number of stations along a line and the passenger
travel time from origin to terminus. Specifically, while a larger
number of stations along a line improves the proximity of the
subway to a wide range of destinations, this larger number of
stations will necessarily slow the passenger travel time of
passengers that do not want to exit the train at a particular
station.
[0005] One conventional approach to solving the two problems of
overcrowded subway train systems and long passenger travel times is
the use of express trains, which are trains that do not stop at
every station along a line. In some of the larger subway systems,
such as those in New York City, Paris, and Seoul, separate railways
and station platforms are provided for the express and local
trains, enabling the express trains to travel the route without
being held up by the slower local trains that stop at each station.
In these systems with separate express lines and stations, in which
the express trains are not slowed by local trains and stops at
local stations, those passengers that board at an express station,
remain on an express train throughout their trip, and exit at an
express station, have the optimum passenger travel time.
[0006] However, many passengers must ride a local train either to
travel to an express station, or to travel from the express station
to their desired destination, or both. If these passengers wish to
take advantage of the express train service, they must make a
transfer between the local and express lines at least once during
their trip. The total travel time for these passengers thus
includes not only the travel time while on the trains, but also the
transfer time involved in changing trains at the express stations.
One can consider this transfer time to be the sum of several
components, including the boarding and deboarding times, the time
required for the passenger to walk between the express and local
platforms (typically on different subway levels), and also the time
spent waiting for the "transfer-to" train to arrive at the station.
Typically, the wait time dominates this transfer time, and can be
considered as a random variable, with a mean value of about 1/2 the
"headway" time of the "transfer-to" train.
[0007] By way of further background, it is known to synchronize the
arrival and departure times of express trains at express stations
with the arrival and departure times of local trains at those
stations, during rush hour periods of the day. For example, the New
York City subway system has been known to schedule their express
subway service to minimize transfer times between express and local
trains, at least during morning rush hour periods. In this way, the
wait time that passengers spend waiting for the "transfer-to" train
to arrive at the station is reduced.
[0008] As evident from this description, however, those subway
systems or portions of subway systems that are limited to only a
single track in each direction of travel have not been able to
provide express service. In such systems, the ultimate speed of
travel of an express train, which as such does not stop at local
stations located between express stations, will eventually
necessarily be limited by the speed of any local train that the
express train catches up to along the route.
[0009] By way of further background, "side tracks" or "sidings" are
used in some railway systems to allow a faster train to pass a
stopped or slower train. FIG. 1a illustrates, in plan view, an
example of a conventional passenger rail station at which faster
trains are allowed to pass slower or stopped trains, using side
tracks. In this example, the two-track system includes main line
2WE for trains traveling "west" to "east" in the view of FIG. 1a,
and main line 2EW for trains traveling "east" to "west". Main line
2WE is disposed adjacent to platform 5WE, at which passenger are
able to board and de-board west-to-east traveling trains, while
main line 2EW is disposed adjacent to platform 5EW, which supports
passenger boarding and deboarding for east-to-west travel. This
conventional station includes side tracks 4WE, 4EW associated with
platforms 5WE, 5EW, respectively. Side tracks 4WE, 4EW can each be
coupled to their respective main tracks 2WE, 2EW, such that a train
traveling along main track 2WE, for example, can switch over to and
travel along side track 4WE at this station, or can instead
continue on main track 2WE. As evident from FIG. 1a, in this
conventional arrangement, a slower train approaching the station
from the west on main track 2WE can switch over to side track 4WE
and stop at platform 5WE, allowing a faster train such as an
express train to remain on main track 2WE and travel past platform
5WE, effectively passing the slower train that is stopped at
platform 5WE on side track 4WE. As such, a two-track subway line
including stations such as the conventional station shown in FIG.
1a can support express and local service.
[0010] Side track facilities are typically more prevalent at
surface rail stations than at subway stations, because the
excavation cost etc. involved in adding a side track at a subway
station is typically prohibitive. For example, as shown in FIG. 1a,
the station must be sufficiently wide (vertical dimension in FIG.
1) to include the two main tracks 2WE, 2EW, two platforms 5WE, 5EW,
two side tracks 4WE, 4EW, and the appropriate spacing on either
side of each of these structures. If an existing two-track system
wished to add express service, the cost of adding side tracks 4WE,
4EW in the manner shown in FIG. 1a is especially prohibitive, and
for that reason is seldom carried out. And even in those surface or
subway systems in which side tracks are provided at stations,
significant wait time is often required for passengers to change
from one train to another, as mentioned above.
[0011] By way of further background, computer algorithms for
optimizing the scheduling of trains are known in the art. U.S. Pat.
No. 6,873,962 B1 describes an automated approach for scheduling
departure times and velocities of trains traveling along a rail
corridor, by deriving and optimizing a cost function that ensures
that all intersections (trains meeting or passing one another)
occur at locations at which side tracks are in place. U.S. Patent
Application Publication No. US 2005/0234757 A1 describes an
automated scheduling system for freight trains, in a railway system
including side tracks to allow faster trains to pass slower or
stopped trains. U.S. Patent Application Publication No. US
2005/0261946 A1 also describes a method and system for calculating
a train schedule plan that operates by optimizing a cost function
to minimize delays at crossing loops and lateness at key locations
along train routes. U.S. Patent Application No. US 2008/0109124 A1
describes a train scheduling method in which placeholders ("virtual
consists") are used to improve the stability of the solution.
[0012] However, each of these conventional train scheduling methods
and systems apply to the scheduling of trains that are not
concerned with allowing passengers to board or de-board at
intermediate stations along the route. In other words, these
scheduling methods do not involve the problem of passenger transfer
from one train to another, nor do they account for trains that
allow for the payload to efficiently board and de-board at any
particular stop along the route. In other words, these conventional
scheduling methods and systems do not solve many of the important
and dominant issues involved in commuter rail systems, particularly
subway systems.
[0013] By way of further background, U.S. Pat. No. 1,604,932
describes a passenger train system in which passenger throughput is
increased by providing trains that are longer than the available
platforms. Some cars in the train stop at the platform of every
station, while other cars in the train stop at the platform only at
alternating stations. The cars and platforms are color-coded, so
that the passengers are aware of the restrictions.
[0014] By way of further background, it is well known in the urban
transportation field that customer demand varies greatly between
peak hours of the day (e.g., morning and evening "rush hours"
during work days) and non-peak hours and days (e.g., weekends,
holidays, and mid-day and night hours of work days). For the case
of a typical rush hour duration of 21/2 hours, twice per work day,
a given subway line operates in a non-rush hour state for on the
order of three-fourths of each workday. One study has shown that
over 80% of the workday passengers of subway lines, worldwide,
occur during rush hour periods. As such, one can roughly determine
that the passenger load per hour of a typical city subway line can
be more than twenty times greater in rush hour periods than in
non-rush hour periods. As such, if the subway operator operates
trains identically during rush hour and non-rush hour periods, the
passenger loading of the trains during non-rush hour periods is
extremely light; conversely, the train utilization during non-rush
hour periods is very low.
[0015] Many subway lines address this inefficiency in subway train
usage by reducing the frequency of train service during non-rush
hour periods. However, this approach is known to even further
depress passenger demand during non-rush hour periods, as some
passengers will use available alternative modes of transportation
rather than endure inordinately long waits at the station. Reduced
frequency of service especially increases the travel time for those
passengers who must make inter-line transfers. Another conventional
approach for improving the efficiency of the subway system in
non-rush hour periods is to shorten the length of the trains, such
that each train has fewer cars (and thus greater utilization of
seats) during non-rush hour periods than it would with full-length
trains. However, the number of operator personnel required in this
approach is essentially the same as if the trains were of full
length. In addition, additional personnel and operational
complexity results from the tasks of coupling and decoupling cars
from trains, parking the decoupled cars, and the like. As such,
considering that a large majority of even the workday is outside of
the rush hours, efficient utilization of transportation
infrastructure, rolling stock, and personnel has not been attained
in conventional subway systems.
BRIEF SUMMARY OF THE INVENTION
[0016] It is therefore an object of this invention to provide a
system and method of operating a subway train system that optimizes
the utilization of subway system resources including the subway
tracks, subway stations, and subway trains, while substantially
reducing passenger travel time for all passengers.
[0017] It is a further object of this invention to provide
synchronized connections between express and local trains,
throughout the year, at each express station in express/local urban
commuter rail systems.
[0018] It is a further object of this invention to provide optimum
connections between express and local trains at each express
station, with minimum passenger transfer time between the express
and local trains.
[0019] It is a further object of this invention to reduce passenger
total travel time at minimal system cost, resulting in reduced
overcrowding of subway trains by improving the passenger throughput
rate of the system.
[0020] It is a further object of this invention to provide such a
system and method that is adapted to new or existing two-track
subway systems.
[0021] It is a further object of this invention to provide such a
system and method of that enables express trains to operate on the
same subway line as local trains, while enabling the express trains
to reduce the travel times of the express passengers.
[0022] It is a further object of this invention to provide such a
system and method in which passenger transfer times at express
stations are minimized.
[0023] It is a further object of this invention to provide such a
system and method in which express service is provided without
requiring the construction of side tracks or other infrastructure
at the express stations.
[0024] It is a further object of this invention to provide such a
system and method that facilitates the changing of trains at
express stations to provide passengers with the opportunity to
further reduce their travel time in exchange for minimal effort on
their part, indeed to reduce their travel time to such an extent
that a passenger can travel along the route at an effective speed
that is faster than the fastest subway train travels along that
route.
[0025] It is a further object of this invention to minimize the
time spent by an arriving train waiting for a train at the station
to leave the station, while providing the additional convenience to
passengers of extra stops along the express route.
[0026] It is a further object of this invention to improve the
utilization of rolling stock and operating personnel during
non-rush hour periods, without significantly impacting the
frequency of service at stops along the route.
[0027] Other objects and advantages of this invention will be
apparent to those of ordinary skill in the art having reference to
the following specification together with its drawings.
[0028] According to one aspect of this invention, the departures
and velocities of express and local subway trains are synchronized
so that the express train arrives at express stations at
approximately the same time as the local service train that is
ahead of the express train on the same track. A novel side track
and transfer system is provided to allow the express train to pass
the local train at the express station, and to allow passengers to
transfer directly between the stopped local and express trains
without deboarding to a platform and waiting at the platform.
[0029] According to another aspect of this invention, the
departures and velocities of express and local subway trains are
synchronized so that the express train arrives at express stations
at approximately the same time as the local service train that is
ahead of the express train on the same track. At the express
station, one or more of the trains transform from providing local
service to providing express service, so that the last of the
trains to arrive at the express station at a given time transforms
from an express train to a local train, with the first one of the
trains arriving at that station at that time transforms from a
local train to an express train. Each passenger remaining on one of
the trains thus travels at express speeds for at least a portion of
the trip.
[0030] According to another aspect of this invention, the
synchronized trains arriving at an express station at approximately
the same time are shuttled at the platform to allow passengers to
transfer from a train that is transforming from express to local
service, to a train that is transforming from local to express
service. These passengers can thus travel at express speeds for all
but the necessary local legs of their trip. Indeed, it is possible
for these transferring passengers to arrive at their eventual
destination after a travel time that is shorter than that of the
fastest train along that route.
[0031] According to another aspect of this invention, the
later-arriving of the synchronized trains arriving at an express
station is scheduled so that it makes an additional stop along its
express leg, thus minimizing time that it must wait for the
earlier-arriving synchronized train to leave the express station
while improving customer convenience.
[0032] According to another aspect of this invention, fewer
stations along the subway line are designated as express stations
during non-rush hour periods than during rush hour periods. In
effect, the interval between express stations is scaled longer, for
example by a multiple of two, three, or four. This scaling of the
express station interval, and thus the scaling of the "group train
dispatching interval", reduces the number of stations at which the
express train passes a local train. By including additional
"semi-express" stations along the scaled express station interval,
and because customer load is lighter during non-rush hour periods,
fewer trains can provide the same frequency of service as during
rush hour periods.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING
[0033] FIG. 1a is a schematic diagram, in plan view, of a
conventional train station with side tracks.
[0034] FIGS. 1b through 1d are schematic diagrams, in plan view, of
the operation of an embodiment of this invention in connection with
a train station with side tracks.
[0035] FIG. 2a is a schematic illustration of a subway line in
connection with which embodiments of the invention are applied.
[0036] FIG. 2b is a plot illustrating the relative travel
velocities of an express train and a local train along the subway
line of FIG. 2a, according to embodiments of this invention.
[0037] FIG. 3a is an electrical diagram, in block form,
illustrating a computer system for scheduling and managing subway
trains on the subway line of FIG. 2a, according to embodiments of
the invention.
[0038] FIG. 3b is a flow diagram illustrating the operation of the
system of FIG. 3a in scheduling and managing subway trains on the
subway line of FIG. 2a, according to embodiments of the
invention.
[0039] FIGS. 3c and 3d are plots illustrating the relative travel
velocities of express trains and local trains along the subway line
of FIG. 2a, according to embodiments of this invention.
[0040] FIGS. 3e through 3h are snapshot views of the subway line of
FIG. 2a, at specific points in time in the operation of that subway
line described in FIGS. 3c and 3d, according to embodiments of this
invention.
[0041] FIGS. 4a through 4c and 4e are schematic diagrams, in plan
view, of an express subway station enabling physical passing and
direct train-to-train passenger transfer according to an embodiment
of the invention.
[0042] FIG. 4d is an elevation view of adjacent subway trains
carrying out direct train-to-train passenger transfer according to
the embodiment of the invention shown in FIGS. 4a through 4c and
4e.
[0043] FIGS. 5a through 5k are schematic diagrams, in plan view, of
an express subway station enabling physical passing and direct
train-to-train passenger transfer according to embodiments of the
invention.
[0044] FIGS. 51 through 5o are snapshot views at specific points in
time in the operation of the subway line described in 4a through
4d, according to embodiments of this invention.
[0045] FIG. 6 is a plot illustrating the relative travel velocities
of trains transforming between providing express service and local
service along a subway line, according to embodiments of this
invention.
[0046] FIGS. 7a through 7c are plots illustrating the operation of
trains transforming between providing express service and local
service along a subway line, according to embodiments of this
invention.
[0047] FIGS. 7d through 7g are snapshot views of the subway line of
FIG. 2a, at specific points in time in the operation of a subway
line, according to conventional operation (FIG. 7d) and to
embodiments of this invention (FIGS. 7e through 7g).
[0048] FIGS. 8a through 8c are schematic diagrams, in plan view,
illustrating the operation of trains making a stop at an express
station, according to an embodiment of the invention.
[0049] FIGS. 9a through 9c are schematic diagrams, in plan view,
illustrating the assignment of semi-express stations along an
interval between express stations, according to an embodiment of
the invention.
[0050] FIGS. 10a through 10g are schematic diagrams, in plan view,
illustrating the operation of trains making a stop at an express
station, according to another embodiment of the invention.
[0051] FIGS. 11a through 11c are schematic diagrams, in plan view,
illustrating the operation of trains making a stop at an express
station, according to another embodiment of the invention.
[0052] FIGS. 12a through 12h are schematic diagrams, in plan view,
illustrating the operation of trains making a stop at an express
station, according to other embodiments of the invention.
[0053] FIGS. 13a and 13b are plan and elevation views,
respectively, of an express station at which the system of FIG. 3a
communicates boarding instructions to passengers, according to
embodiments of the invention.
[0054] FIGS. 13c and 13d are views of the content of graphics
displays at the station of FIGS. 13a and 13b by way of which
boarding instructions are communicated to passengers, according to
embodiments of the invention.
[0055] FIGS. 14a through 14d are timeline plots illustrating train
travel times as varying spatially along a subway line, according to
embodiments of the invention.
[0056] FIGS. 15a through 15d are timeline plots illustrating train
travel times as varying spatially along a subway line and varying
with the time of day, according to embodiments of the
invention.
[0057] FIGS. 16a through 16d are timeline plots illustrating train
travel times as varying spatially along a subway line, varying with
the time of day, and varying with the day of the week/month/year,
according to embodiments of the invention.
[0058] FIGS. 17a through 17c are plots illustrating the elongation
of express station intervals during non-rush hour periods,
according to embodiments of this invention.
[0059] FIG. 17d illustrates the deployment of express stations for
various alternatives of scaling factors for non-rush hour periods,
according to embodiments of this invention.
DETAILED DESCRIPTION OF THE INVENTION
[0060] This invention will be described in connection with its
embodiments, as implemented into an urban commuter rail system in
which at least a significant portion of the system is an
underground subway system. These embodiments are described in this
specification because it is contemplated that this invention will
be especially beneficial when utilized in such an application.
However, it is contemplated that this invention can also provide
similar important benefits if implemented in other applications and
environments. Accordingly, it is to be understood that the
following description is provided by way of example only, and is
not intended to limit the true scope of this invention as
claimed.
[0061] FIG. 2a schematically illustrates the context of embodiments
of this invention in connection with subway line SLINE, which
travels from an origin to a terminus. For purposes of this
contextual description, subway line SLINE will be discussed in
connection with a single direction of travel (west to east in FIG.
2a); of course, subway line SLINE in fact supports travel in both
directions (west to east, and east to west, in FIG. 2a). In the
example of FIG. 2a, seven express stations E0 through E6 are shown
as located along subway line SLINE, with express station E0
corresponding to the origin, and express station E6 corresponding
to the terminus, of subway line SLINE in its west-to-east direction
of travel. As shown in FIG. 2a, each of intervals I1 through I6 is
defined as the length of subway line SLINE between respective pairs
of express stations E0 through E6 (e.g., interval I1 is the
interval between express stations E0 and E1, interval I2 is the
interval between express stations E1 and E2, and so on). In this
example of subway line SLINE, local stations are present along each
interval I1 through 16; for example, four local stations are
located along interval I1 between express station E0 and express
station E1. Express stations E0 through E6 also serve as local
stations (specifically, the local stations numbered 0, 5, 10, 15,
etc. shown in FIG. 2a), in this example.
[0062] FIG. 2b illustrates the theoretical travel time for an
express train EXP and a local train LOC along subway line SLINE, in
a single direction (e.g., west to east). The timing illustrated in
FIG. 2b shows express train EXP and local train LOC leaving the
origin of subway line SLINE (express station E0) at essentially the
same time (0 minutes in FIG. 2b), but with express train EXP
immediately leading local train LOC. In this example, local train
LOC will stop at each local station along each interval I1 through
I6 of subway line SLINE, while express train EXP stops only at
express stations E1 through E6. Because express train EXP does not
make the local stops while local train LOC does, express train EXP
reaches terminus express station E6 earlier than does local train
LOC. In this example, express train EXP reaches terminus E6 after
thirty minutes of travel, while local train LOC reaches terminus E6
after sixty minutes of travel. Express train EXP may not
necessarily be traveling at faster instantaneous velocities along
subway line SLINE than local train LOC, but its higher effective
travel velocity may result simply because it does not stop at the
local (i.e., non-express) stations along subway line SLINE. In any
case, the overall travel time of express train EXP along subway
line SLINE is shorter than that of local train LOC.
[0063] However, if subway line SLINE is essentially a two-track
line, such that one railway track carries trains travelling in one
direction and the other track carries trains travelling in the
other direction, then the theoretical timing illustrated in FIG. 2b
is valid only if express train EXP does not catch up to any local
train before reaching terminus E6. In the example of FIG. 2b, this
condition holds so long as no local train left origin express
station E0 less than thirty minutes prior to time 0 at which
express train EXP left origin express station E0. Otherwise,
express train EXP would catch up to that earlier-leaving local
train, and its travel velocity from that point forward would be
limited by the travel velocity and local station stops of that
earlier-leaving local train. In other words, because subway line
SLINE is a two-track line, a faster traveling express train is
unable to pass a slower moving local train. To avoid this situation
of express trains being limited by local train service, trains must
be separated far enough in time that no express train can catch up
to the immediately preceding local train. Of course, it is
generally impractical to operate a subway system of any length or
ridership level in which trains are separated by such long times,
for example no less than thirty minutes as in the case of FIG.
2b.
[0064] Because of this limitation, most conventional two-track
lines in modern subway systems do not support express train
service. Rather, every train along these conventional subway lines
operates as a local train, and the passenger throughput and travel
convenience are limited--every subway passenger must endure the
time required for the train to make every local stop along his or
her trip. Typically, the cost of providing side tracks as described
above relative to FIG. 1a is prohibitive in the subway context,
especially if a subway operator wishes to retrofit an existing
two-track station to provide express service (for example, to
alleviate overcrowding of trains in local-only service).
[0065] It has been discovered, according to this invention, that
express subway service can be provided within a two-track system,
in a manner that requires, at most, a much reduced cost relative to
the cost of retrofitting stations to include conventional side
tracks; in some embodiments of this invention, as will become
apparent from the following description, express service can be
provided in a subway system without incurring any construction or
infrastructure costs. This invention thus provides important
benefits to both the subway operator and the subway passenger
community, such benefits including improved passenger throughput
that results in reduced passenger travel times and reduced
passenger overcrowding, improved utilization of existing subway
infrastructure, and enhanced passenger autonomy in managing subway
travel.
[0066] Synchronization of Express and Local Trains
[0067] As evident from the previous description, in order to
provide reasonable express subway service on a two-track subway
line (i.e., one track for each direction of travel), the ability of
an express train to effectively pass a slower traveling local train
must be provided. As mentioned above, it is contemplated that
express subway trains may not actually be traveling at faster
instantaneous velocities than local trains, but may instead travel
at faster effective travel velocities because these express train
do not stop at local (i.e., non-express) stations.
[0068] According to embodiments of the invention, express stations
are periodically defined as locations along a subway line at which
express subway trains and local subway trains both make stops, at
which passengers may board and de-board both local and express
trains, and at which passengers may transfer from a local train to
an express train. Also according to embodiments of the invention,
the scheduling of the express and local trains is synchronized
relative to each other so that the faster-traveling express trains
catch up to slower-traveling local trains at express stations only.
And at those express stations, express trains are permitted to pass
local trains, either physically or "virtually", even though the
subway line may be constructed as a two-track subway line with only
one track provided for travel in each direction. The particular
manner in which the physical or virtual passing of trains is
carried out at these stations will be described in detail below in
connection with the specific embodiments of this invention.
[0069] According to embodiments of this invention, the scheduling
of the express and local trains to arrive effectively
simultaneously at express stations is carried out by a computerized
system that is constructed, programmed, and operated to accomplish
that scheduling task. FIG. 3a illustrates, according to an example
of an embodiment of the invention, the construction of subway
scheduling and operating system ("system") 20. In this example,
system 20 is as realized by way of a computer system including
workstation 21 connected to server 30 by way of a network. Of
course, the particular architecture and construction of a computer
system useful in connection with this invention can vary widely.
For example, system 20 may be realized by a single physical
computer, such as a conventional workstation or personal computer,
or alternatively by a computer system implemented in a distributed
manner over multiple physical computers. Accordingly, the
generalized architecture illustrated in FIG. 3a is provided merely
by way of example.
[0070] As shown in FIG. 3a and as mentioned above, system 20
includes workstation 21 and server 30. Workstation 21 includes
central processing unit 25, coupled to system bus BUS. Also coupled
to system bus BUS is input/output interface 22, which refers to
those interface resources by way of which peripheral functions P
(e.g., keyboard, mouse, display, etc.) interface with the other
constituents of workstation 21. Central processing unit 25 refers
to the data processing capability of workstation 21, and as such
may be implemented by one or more CPU cores, co-processing
circuitry, and the like. The particular construction and capability
of central processing unit 25 is selected according to the
application needs of workstation 21, such needs including, at a
minimum, the carrying out of the functions described in this
specification, and also including such other functions as may be
executed by computer system 20. In the architecture of system 20
according to this example, system memory 24 is coupled to system
bus BUS, and provides memory resources of the desired type useful
as data memory for storing input data and the results of processing
executed by central processing unit 25. According to this
embodiment of the invention, workstation 21 also includes program
memory 34, which is a computer-readable medium that stores
executable computer program instructions according to which the
operations described in this specification are carried out. In this
embodiment of the invention, these computer program instructions
are executed by central processing unit 25, for example in the form
of an interactive application, to generate schedules for the
express and local trains that are to travel on subway line SLINE,
and in some instances, to manage the operation of subway line SLINE
according to that schedule and in response to actual conditions
encountered during operation. These computer program instructions
can result in data and results that are displayed or output by
peripherals I/O in a form useful to the human user of workstation
21, or that result in operational signals to be communicated to the
trains and stations. Of course, this memory arrangement is only an
example, it being understood that the particular arrangement and
architecture of memory resources within workstation 21 may vary,
for example by implementing data memory and program memory in a
single physical memory resource, or distributed in whole or in part
outside of workstation 21.
[0071] Network interface 26 of workstation 21 is a conventional
interface or adapter by way of which workstation 21 accesses
network resources on a network. In this embodiment of the
invention, the network to which network interface 26 is coupled may
be a local area network, or may be a wide-area network such as an
intranet, a virtual private network, or the Internet. As shown in
FIG. 3a, one or more of the network resources accessible by
workstation 21, either directly or indirectly, includes
train/station interface 28 that receives inputs via bus TRN_I/O
from or concerning each of the subway trains in subway line SLINE
(or throughout the subway system including subway line SLINE), that
receives inputs via bus STA_I/O from or concerning each of the
subway stations along subway line SLINE (or throughout the subway
system including subway line SLINE), and that also communicates
signals to those subway trains and stations via buses TRN_I/O and
STA_I/O. The signals communicated from these trains and stations
are received by interface 28 and, in this example, are stored in a
memory resource that resides locally within workstation 21, or that
is accessible to workstation 21 over the network, via network
interface 26.
[0072] As shown in FIG. 3a, the network resources to which
workstation 21 has access via network interface 26 also include
server 30, which resides on a local area network, or a wide-area
network such as an intranet, a virtual private network, or the
Internet, and which is accessible to workstation 21 by way of one
of those network arrangements and by corresponding wired or
wireless (or both) communication facilities. In this embodiment of
the invention, server 30 is a computer system, of a conventional
architecture similar, in a general sense, to that of workstation
21, and as such includes one or more central processing units,
system buses, and memory resources, network interface functions,
and the like. In addition, library 32 is also available to server
30 (and perhaps workstation 21 over the local area or wide area
network), and stores such archival or reference information as may
be useful in system 20. Library 32 may reside on another local area
network, or alternatively be accessible via the Internet or some
other wide area network. It is contemplated that library 32 may
also be accessible to other associated computers in the overall
network.
[0073] Of course, the particular memory resource or location at
which persistent and temporary data, library 32, and program memory
34 physically reside can be implemented in various locations
accessible to the computational resources of system 20. For
example, data and program instructions may be stored in local
memory resources within workstation 21, within server 30, or in
memory resources that are network-accessible to these functions. In
addition, each of the data and program memory resources can itself
be distributed among multiple locations, as known in the art. It is
contemplated that those skilled in the art will be readily able to
implement the storage and retrieval of the applicable measurements,
models, and other information useful in connection with this
embodiment of the invention, in a suitable manner for each
particular application.
[0074] According to this embodiment of the invention, program
memory within system 20, whether within workstation 21 or within
server 30, stores computer instructions that are executable by
computational functions within central processing unit 25 and
server 30, respectively, to carry out the functions described in
this specification, by way of which the departure and operation of
subway trains traveling along subway line SLINE are scheduled and
managed. These computer instructions may be in the form of one or
more executable programs, or in the form of source code or
higher-level code from which one or more executable programs are
derived, assembled, interpreted or compiled. Any one of a number of
computer languages or protocols may be used, depending on the
manner in which the desired operations are to be carried out. For
example, these computer instructions may be written in a
conventional high level language, either as a conventional linear
computer program or arranged for execution in an object-oriented
manner. These instructions may also be embedded within a
higher-level application. For example, the scheduling and operation
applications can reside entirely within program memory 34 of
workstation 21, such that workstation 21 itself executes the method
and processes described in this specification in connection with
the embodiments of this invention, with server 30 performing
network and data retrieval operations. According to another
example, an executable web-based application can reside at program
memory within server 30 and client computer systems such as
workstation 21, receive inputs from the client system in the form
of a spreadsheet, execute algorithms modules at a web server, and
provide output to the client system in some convenient display or
printed form, or output to trains and stations by way of signals
communicated via interface 28. Other arrangements may of course
also be constructed and operated within a system architecture such
as that of system 20 shown in FIG. 3a, or according to other
architectures. It is contemplated that those skilled in the art
having reference to this description will be readily able to
realize, without undue experimentation, this embodiment of the
invention in a suitable manner for the desired installations.
Alternatively, these computer-executable software instructions may
be resident elsewhere on the local area network or wide area
network, or downloadable from higher-level servers or locations, by
way of encoded information on an electromagnetic carrier signal via
some network interface or input/output device. The
computer-executable software instructions may have originally been
stored on a removable or other non-volatile computer-readable
storage medium (e.g., a DVD disk, flash memory, or the like), or
downloadable as encoded information on an electromagnetic carrier
signal, in the form of a software package from which the
computer-executable software instructions were installed by system
20 in the conventional manner for software installation.
[0075] Referring now to FIG. 3b, the generalized operation of
system 20 in carrying out the scheduling and operation of subway
line SLINE, and its trains and stations, according to this
invention will be described. The specific operations involved in
connection with the embodiments of this invention will, of course,
vary from embodiment to embodiment, and will be apparent to those
skilled in the art having reference to this specification. However,
it is contemplated that the generalized operation illustrated in
FIG. 3b will provide context for the manner in which the automated
and computerized control can be realized, in a manner that is
well-suited for providing the benefits of this invention.
[0076] The generalized flow diagram of FIG. 3b illustrates that the
overall schedule and deployment of express and subway trains
according to this embodiment of the invention is based on various
sources of data and information, all of which are stored in library
32 or some other memory resource of system 20. Passenger data
source 33 includes data regarding the number of passengers using
subway line SLINE, data regarding the numbers of passengers that
embark and disembark subway line SLINE at each of the various
stations along the line, data regarding how those numbers of
passengers vary relative to the time of day and also from day to
day, and other similar data that may be useful in defining a subway
train line schedule. Train data source 35 includes data indicating
the number of subway trains and cars available for subway line
SLINE, the number of passengers each train and car can carry
comfortably or safely (or both, should those numbers differ from
one another), data regarding the maximum and optimal (desired)
velocities at which the trains and cars can travel along a subway
line, stopping distances, and other similar data regarding the
train resources that may be useful in defining a subway train
schedule. Station data source 37 include data indicating the
locations of stations along subway line SLINE, the infrastructure
attributes of each of those stations (e.g., length of platform,
passenger handling capacity, presence of support infrastructure,
etc.), whether connections to other subway lines are located at
those stations and the passenger demand for such connections, and
other similar data regarding the stations along subway line SLINE
that may be useful in defining a subway train schedule. Data from
these data sources 33, 35, 37, as well as data regarding other
parameters useful to the scheduling process, are accessed or
otherwise available to system 20 in carrying out the scheduling
process of embodiments of the invention.
[0077] In this high-level description of FIG. 3b, process 34 is
carried out by system 20 to define which stations along subway line
SLINE are to be express and local stations, and which stations are
to be local stations only. In some cases, the selection of express
stations along subway line SLINE may be pre-determined based on
other criteria, such as by upper management of the subway station,
the manner in which the particular stations may be constructed (to
the extent not represented within station data source 37), customer
surveys, or the like. Absent such external restrictions, process 34
is performed by computational resources within system 20 executing
program instructions to optimize the selection of express stations,
for example in an automated or "artificial intelligence" manner.
For example, operational criteria may be used to define a cost
function, such that iterative or Monte Carlo evaluation of the cost
function may be performed using a number of trial selections of
express stations, in order to evaluate the optimum assignment based
on passenger data 33, train data 35, and station data 37.
Preferably, parameters representative of passenger throughput,
passenger travel time, passenger comfort (i.e., avoiding
overcrowded conditions), and subway train utilization, will be
reflected in such a cost function. It is contemplated that those
skilled in the art having reference to this specification will be
able to apply conventional AI and other evaluation techniques to
define the express stations for the current information, in this
process 34.
[0078] In process 36, computational resources within system 20
execute program instructions to define the number and frequency of
express and local trains to be scheduled along subway line SLINE
over time within a day, and as that schedule may vary from day to
day. Similarly as process 34 described above, it is contemplated
that process 36 is also carried out in an automated manner, for
example by evaluating a cost function that expresses criteria
involved in defining the numbers, lengths, and arrangement of
express trains within the schedule. As will be evident from some
embodiments of this invention described below, definition process
36 can include the defining of "group" subway trains, with the
express portion substantially longer than the local portion.
Constraints on the number of express trains are contemplated to
depend on the various data elements described above and provided
from data sources 33, 35, 37. Preferably and as described above,
parameters representative of passenger throughput, passenger travel
time, passenger comfort (i.e., avoiding overcrowded conditions),
and subway train utilization, will be reflected in the cost
function that is optimized in process 36. It is contemplated that
those skilled in the art having reference to this specification
will be able to apply conventional AI and other evaluation
techniques to define the number and frequency of express trains for
the current information relative to subway line SLINE, in this
process 36.
[0079] Alternatively to processes 34, 36, the definition of express
stations and the numbers and frequencies of express trains can
instead be defined a priori by subway system management. While it
is contemplated that such definition of these resources will, in
general, not be optimized for all of the objectives of passenger
throughput, passenger travel time, passenger comfort, and subway
train utilization, and the like, the overall scheduling and
operational process of this invention can still operate within such
an environment to optimize these and other attributes within those
constraints.
[0080] In process 38, computational resources within system 20
operate to derive a schedule for subway line SLINE over time, for
the express stations defined in process 34 (or otherwise) and for
the number and frequency of express trains defined in process 36
(or otherwise). According to embodiments of this invention, the
schedule derived in process 38 synchronizes the operation of
express and local trains so that express and local trains meet in
time only at express stations. As mentioned above and as will be
evident from the following description of embodiments of this
invention, express stations allow for express trains to pass the
slower-traveling local trains, either physically or virtually;
conversely, at locations other than express stations along subway
SLINE, an express train that catches up to a local train will have
its travel time constrained by the speed of and stops made by the
local train, at least until both trains reach the next express
station. Optimal operation of subway line SLINE is thus
contemplated to be achieved with express and local trains traveling
in the same direction meeting only at express stations; in process
38, as a result, the departures and travel velocities of express
trains will be defined in a manner that is synchronized with the
schedule being followed by the local train that is ahead of the
express train along subway line SLINE. It is contemplated that
those skilled in the art having reference to this specification
will be able to apply conventional AI and other evaluation
techniques, for example by evaluating a cost function that
expresses criteria involved in deriving the schedule, to define the
operational schedule of subway line SLINE, including departure
times and travel velocities, for the current information relative
to subway line SLINE, in this process 38. In such an example, the
cost function may express some measure related to passenger travel
time along subway line SLINE, in an average, cumulative, or some
other statistical sense, such that the schedule is derived, in
process 38, by minimizing this measure of passenger travel
time.
[0081] Referring to FIG. 3c, the manner in which express and local
trains are synchronized with one another in an optimal schedule
derived in process 38, according to embodiments of this invention,
will now be described. FIG. 3c is a plot of train travel along
subway line SLINE, presented in a form in which distance follows
the horizontal axis and time follows the vertical axis (increasing
time in the downward direction). The travel of express trains EXP1
through EXP4 and local trains LOC0 through LOC3 along subway line
SLINE is illustrated in FIG. 3c. As evident from FIG. 3c, express
trains EXP1 through EXP4 travel at effectively twice the travel
velocity of local trains LOC0 through LOC3, in large part because
local trains LOC0 through LOC3 stop at local stations (not shown)
between express stations. This difference in speed of course means
that faster express trains EXP1 through EXP4 will catch up to
slower local trains LOC0 through LOC3 at some point along subway
line SLINE. But because subway line SLINE is a two-track line, one
track in each direction of travel, some provision must be made to
allow express trains EXP1 through EXP4 to make passes.
[0082] According to embodiments of this invention, express trains
EXP1 through EXP4 are synchronized with local trains LOC0 through
LOC3 in the sense that express trains EXP1 through EXP4 catch up to
local trains LOC0 through LOC3 only at express stations E0 through
E3. For example, local train LOC1 leaves express station E0 at an
earlier time (time t1) than express train EXP2 leaves express
station E0 (time t2), yet both arrive at express station E1 at the
same time (time t3). Similarly, express train EXP3 catches up to
the next previous local train LOC0 at express station E2 (at time
t4). The other trains traveling along subway line SLINE proceed in
a similar manner. Of course, in order for the schedule of FIG. 3c
to hold, provision must be made for express trains EXP1 through
EXP4 to pass local trains LOC0 through LOC3. As such, in the
schedule of FIG. 3c, pass points 1P10 through 1P43 are shown in
FIG. 3c as occurring at express station E1 (e.g., pass point "1P10"
expressing that at express station E1, express train EXP1 is
passing local train LOC0), at times t2 through t5. Similarly, FIG.
3c shows pass points 2P20 through 2P42 occurring at express station
E2, and pass point 3P30 occurring at express station E3. Each of
the pass points 1P10 etc. in FIG. 3c should be considered as
"space-time" points, as they each indicate a particular spatial
point at a particular time (e.g., pass points 1P10 and 1P21 are at
the same point in space, namely express station E1, but at
different times t2, t3, respectively).
[0083] While the time scale and distance scale are shown as
constant along the axes in FIG. 3c, such that express stations E0
through E3 (and time intervals t1 through t6) appear at uniform
intervals relative to one another, it is to be understood that such
uniformity is not necessarily the case. As such, in the actual
operation of the schedule of subway line SLINE as shown in FIG. 3c,
express trains EXP1 through EXP4 and local trains LOC0 through LOC3
do not necessarily travel at a constant velocity. Rather, in order
for the synchronized arrival of express trains EXP1 through EXP4
and local trains LOC0 through LOC3 only at express stations E1
through E3, as shown in FIG. 3c, it may be necessary for the
instantaneous velocities of these trains to vary from interval to
interval. In particular, embodiments of this invention contemplate
that the instantaneous velocity of express trains EXP1 through EXP4
will vary from interval to interval so that their arrival times at
express stations E1 through E3 are synchronized with those of local
trains LOC0 through LOC3.
[0084] FIG. 3d illustrates the case in which the distance (either
in miles or in number of intervening local stops, or both) between
express stations varies from interval to interval. For example, the
time axis of FIG. 3 is at a constant scale along its length, by way
of constant intervals .DELTA.t between each time point, however the
distance intervals vary between express stations. In this example,
interval I.sub.3 between express stations E2 and E3 is longer than
interval I.sub.2 between express stations E1 and E2, however. In
this case, the average velocity of a local train traveling from
express station E0 to express station E3 is the same as that in
FIG. 3c (i.e., local train LOC0 leaves express station E0 at time
t=0 and arrives at express station E3 at time t6), as is the
average velocity of an express train (i.e., express train EXP3
leaves express station E0 at time t3 and arrives at express station
E3 at time t6). However, within the various intervals, the interval
velocity of each express train is governed by the interval velocity
of a local train ahead of that express train over that
interval.
[0085] FIG. 3d illustrates this governing relationship, relative to
local train LOC0. In this example, an express train leaves express
station E0 at the end of each time interval .DELTA.t following time
t=0, followed immediately by a local train as before. The interval
velocity of local train LOC0 over the first express interval
I.sub.1 will depend on various factors such as the instantaneous
velocities at which local train LOC0 travels between stops, the
stop time at each local station over the interval, and the like. In
any event, the interval velocity of the next express train EXP1
over express interval I.sub.1 is governed by the interval velocity
of local train LOC0 over that distance, such that express train
EXP1 meets and passes local train LOC0 at express station E1 (pass
point 1P10), and therefore leaves express station E1 before local
train LOC0. Over the next shorter interval I.sub.2 from express
station E1 to express station E2, local train LOC0 travels at its
interval velocity, which in this example is slightly faster than
its interval velocity over interval I.sub.1 (as evidenced by the
slightly flatter line in the plot of FIG. 3d over this interval).
The interval velocity of express train EXP2 over interval I.sub.2
is governed by the interval velocity of local train LOC0 over this
interval; as evident from FIG. 3d, this interval velocity is also
faster than its interval velocity over interval I.sub.1 so as to
meet and pass local train LOC0 at express station E2 (pass point
2P20). Express train EXP 2 leaves express station E2 ahead of local
train LOC0 in this example, so that local train LOC0 leads express
train EXP3 over the next interval I.sub.3. Over that interval
I.sub.3, the interval velocity of local train LOC0 increases
further in this example (as evidenced by the flatter line in the
plot of FIG. 3d for local train LOC0 over this interval I.sub.3);
the interval velocity of express train EXP3 also increases over
interval I.sub.3, so that express train EXP3 meets local train LOC0
at express station E3 at time t6 as shown. As such, it is the
velocity of local trains LOC along subway line SLINE that governs
the velocity of the following express trains EXP, so that the
synchronized meeting and passing of express and local trains occurs
only at express stations, according to embodiments of this
invention.
[0086] This operation of subway line SLINE according to embodiments
of this invention can be further described in connection with the
schematic views of subway line SLINE shown in FIGS. 3e through 3h.
These FIGS. 3e through 3h can be considered as plan views, as
though looking down on subway line SLINE from above (and through
the earth above subway line SLINE). FIG. 3e illustrates the state
of subway line SLINE at a point in time in which local trains T0
through T6 are located along subway line SLINE between express
stations E0 and E3, with the first local train T0 at express
station E3 and local train T6 at the farthest-west express station
E0. At the point in time shown in FIG. 3e, express train
{circumflex over (T)}0 is beginning the trip along subway line
SLINE, at express station E0. At the snapshot in time shown in FIG.
3e, local train T5 is located between express stations E0 and E1,
local train T3 is located between express stations E1 and E2, and
local train T1 is located between express stations E2 and E3.
[0087] FIG. 3f illustrates subway line SLINE at the point in time
at which local train T0 has reached express station E6. In other
words, in time between that shown in FIG. 3e and that shown in FIG.
3f, local train T0 (and all other local trains) have traveled the
distance of three express intervals. Meanwhile, during this same
time interval, express train {circumflex over (T)}0 has traveled
six express intervals, and as such has caught up to local train T0
at express station E6. At the express stations E1 through E5
encountered by express train {circumflex over (T)}0 during this
time, express train {circumflex over (T)}0 passed one of local
trains T5 through T1, respectively. During this same time interval,
the pair of express train {circumflex over (T)}1 and local train T7
were dispatched from express station E0 at a time delay .DELTA.t
following the departure of express train {circumflex over (T)}0 and
local train T6. Express train {circumflex over (T)}2 and local
train T8 left express station E0 at time 2.DELTA.t after trains
{circumflex over (T)}0 and T6 departed, trains {circumflex over
(T)}2 and T8 departed at time 3.DELTA.t after trains {circumflex
over (T)}0 and T6 departed, and so on up to the pair of express
train {circumflex over (T)}5 and local train T11 departing express
station E0 after a time delay of 5.DELTA.t after trains {circumflex
over (T)}0 and T6 departed. During the interval between the
snapshot of FIG. 3e and that of FIG. 3f, each of express trains
{circumflex over (T)}1 through {circumflex over (T)}5 have passed
or caught up to corresponding local trains T2 through T11. At the
time shown in FIG. 3f, express train {circumflex over (T)}6 and
local train T12 are at express station E0 and ready to depart.
[0088] FIG. 3g illustrates the portion of subway line SLINE from
express station E0 through express station E3, at the time
corresponding to that shown in FIG. 3f, in more detail. The point
in time shown in FIG. 3g corresponds to that at which the express
trains {circumflex over (T)}3 through {circumflex over (T)}6 have
not yet passed their respective local trains T6 through T12,
respectively. As evident in FIG. 3g, express trains {circumflex
over (T)}3 through {circumflex over (T)}6 arrive at express
stations E0 through E3 shortly after the local trains T6, T8, T10,
T12 that they are passing, respectively. FIG. 3h illustrates the
same situation as shown in FIG. 3g, except in the case in which the
distances between express stations E0 through E3 is not uniform
(i.e., as in the plot of FIG. 3d). As evident in FIG. 3h, this
situation is managed by modulating the interval velocities of the
trains, as described above.
[0089] In connection with this invention, scheduling process 38
derives a schedule in which express trains and local trains meet
one another, when traveling in the same direction, only at express
stations. It is contemplated that the manner in which scheduling
process 38 is executed can readily define and optimize the schedule
by selecting and modulating the departure times and travel
velocities of the express trains as governed by the departure times
and travel velocities of the local trains. Conventional computer
operations are contemplated to be readily capable of performing
such optimization, given the constraints presented by the
synchronization requirements of embodiments of this invention. The
manner in which express trains physically or virtually pass the
local trains at each of the pass points P in FIG. 3c will be
described in detail in this specification, in connection with the
particular embodiments.
[0090] Referring back to FIG. 3b, according to this generalized
method, it is contemplated that the schedule derived in process 38
may be able to be further optimized by changing the relative
densities of express and local trains along subway line SLINE, or
even by redesignating some stations as express stations or as local
stations, as the case may be. As such, and as shown in FIG. 3b,
further iterations of processes 34, 36 may be performed in light of
the optimal schedule derived in the most recent instance of process
38. It is contemplated, therefore, that those skilled in the art
having reference to this specification will be able to comprehend
such iteration in their particular arrangement of the overall
process, again according to conventional optimization
techniques.
[0091] It is contemplated that processes 34, 36, 38 shown in FIG.
3b will be carried out to derive an operational schedule under one
set of operating conditions, for example the high demand conditions
of "rush hour" commute periods, as such periods are especially
challenging for operation of subway lines in modern urban
environments. According to another embodiment of this invention,
FIG. 3b illustrates optional process 39, in which a second schedule
is derived for use in non-rush hour time periods. It is
contemplated, as will be described in further detail below, that
passenger data 33, train data 35, and station data 37 may indicate
that the optimization of the operating schedule may differ greatly
in such non-rush hour periods than during rush hour periods. As
such, according to that alternative embodiment of the invention, it
may be advantageous from the standpoint of train utilization
efficiency and also passenger convenience.
[0092] In process 40, the results of the final instance of
processes 38, 38' are communicated to passengers. It is
contemplated that process 40 can be carried out in various ways,
including the generation of printed schedules, online schedules,
push-transmissions to Internet-capable devices, and the like. It is
also specifically contemplated, in connection with embodiments of
this invention, that the derived schedule will be communicated to
passengers, in process 40, by way of video displays at stations
along subway line SLINE, and video displays on the trains
themselves. To the extent that communication process 40 is
performed electronically, for example to stations and trains, it is
contemplated that system 20 will provide those communications via
train/station interface 28 (FIG. 3a) and buses STA_I/O and TRN_I/O.
According to another example, it is contemplated that interactive
"e-tickets" may be sold and communicated by the subway operator,
enabling real-time communication with passengers regarding
scheduling, car and platform assignments, and the like. The
particular manner in which the schedule is communicated to
passengers in process 40 can, of course, vary widely and may take
any or all of these approaches and also those communications
technologies that may be developed in the future.
[0093] Also as shown in FIG. 3b, according to this generalized
method, it is contemplated that, during operation, the conditions
along subway line SLINE may require changes in the schedule of one
or more trains in mid-course, or for the remainder of the day. Data
regarding the current real-time status of trains and stations along
subway line SLINE are acquired by system 20, for example via buses
STA_I/O, TRN_I/O and station/train interface 28. In this
generalized operation of embodiments of this invention, operational
data 41 are communicated in this manner or otherwise to system 20,
and in process 42, computational resources within system 20 execute
program instructions to adjust departure times and running
velocities of trains along subway line SLINE to optimize its
operation, in light of the previous optimization and the current
conditions. For example, system 20 may receive inputs corresponding
to the current location and status of each of the trains along
subway line SLINE at a given instant in time and can compare that
feedback data to expected or desired locations and status of the
trains according to the current schedule; the error between the
actual and expected positions of the train along subway line SLINE
can then indicate the nature and magnitude of changes to be made to
the operation of the trains, for example by modulating
instantaneous velocities of one or more of the trains, or by
adjusting the stop times of one or more of the trains at one or
more of the stations along subway line SLINE. As shown in FIG. 3b,
such adjustments are then used in another instance of process 40,
so that the changes in the schedule are communicated as appropriate
to affected and potentially affected passengers.
[0094] System 20 and its operation, as described above in
connection with FIGS. 3a and 3b, are presented in this
specification by way of example, and in a generalized manner. It is
contemplated that many variations and alternatives to this system
and its operation as described above will be apparent to those
skilled in the art having reference to this specification, in their
implementation of this invention in particular installations. It is
contemplated that such variations and alternatives will be within
the scope of this invention as claimed.
[0095] Conventional Side-Track Subway Station
[0096] According to an embodiment of the invention, the
synchronized scheduling of express and local subway trains, as
described above in connection with FIGS. 3a through 3h, can be
implemented for subway lines having conventional side-track
facilities at express stations, such conventional side-track
facilities described above in connection with FIG. 1a. Referring
now to FIGS. 1b through 1d, an example of the operation of an
embodiment of the invention in connection with such a conventional
side-track station will now be described.
[0097] FIG. 1b illustrates express station E.sub.x at a point in
time in which an earlier-arriving eastbound local train LOC.sub.0
has arrived at station E.sub.x, and has switched over to side-track
4WE, at which time passengers may board and de-board local train
LOC.sub.0 via platform 5WE. While local train LOC.sub.0 is stopped
at platform 5WE in this manner, later arriving express train
EXP.sub.0 arrives at platform 5WE along track 2WE, as shown in FIG.
1c. At the point in time shown in FIG. 1c, passengers can board and
de-board express train EXP.sub.0 from platform 5WE; in addition,
passengers can transfer between local train LOC.sub.0 and express
train EXP.sub.0 via platform 5WE, as shown. Following the time
required for this boarding and transfer process, express train
EXP.sub.0 then leaves express station E.sub.x ahead of local train
LOC.sub.0, as shown in FIG. 1d; in this manner, express train
EXP.sub.0 physically passes local train LOC.sub.0 at express
station Ex. In addition, if the express passenger demand is
sufficient that multiple express trains are scheduled to pass local
train LOC.sub.0 at this station E.sub.x (such multiple-express
train groups will be described in further detail below), another
express train EXP.sub.1 can also arrive at platform 5WE while local
train LOC.sub.0 remains stopped along side track 4WE as shown in
FIG. 1d. In this manner, this additional express train EXP.sub.1
can also pass local train LOC.sub.0, and allow passenger to and
from local train LOC.sub.0 and from platform 5WE in the manner
illustrated in FIG. 1c.
[0098] Synchronization of the express and local train schedules so
that express trains EXP catch up to local trains LOC only at
express stations, as described above in connection with FIGS. 3a
through 3h, ensures the shortest possible travel times for the
express trains EXP along subway line SLINE, while optimizing the
use of local trains LOC and minimizing passenger wait times for
those making transfers between the trains at express stations. It
is contemplated that this embodiment of the invention will thus
improve the utilization of existing subway train and station
infrastructure, by increasing the passenger throughput of the
subway line. In addition, as passenger throughput increases and
express passenger travel times decrease, it is contemplated that
overcrowding of the subway trains can be reduced, if not
eliminated, through the synchronization method of this
invention.
[0099] Side-by-Side Subway Station
[0100] As described above in connection with FIGS. 1b through 1d,
embodiments of this invention can be used with side track stations
of conventional construction to enable express trains to physically
pass local trains along a two-track subway line. However, it is
believed that few existing subway stations in the world provide
side-track facilities such as those shown in FIGS. 1b through 1d.
It is also believed, as described above, that the cost of
retro-fitting (or originally constructing) subway stations to have
such conventional side-tracks is prohibitive. In addition, the
passenger transfer times at such stations, via the intervening
platform, is contemplated to be significant at these conventional
side-track equipped stations.
[0101] According to another embodiment of the invention, the
express subway stations are constructed so that direct
train-to-train passenger transfers are possible, reducing the
duration of express station stop times and also minimizing the
footprint of the express station (and thus the construction or
retrofit cost). In addition, according to this embodiment of the
invention, the ability for an express subway train to pass a local
subway train, and to permit passengers to transfer directly between
the local and express trains, is facilitated. As described above,
the scheduling of the express and local trains is synchronized
relative to each other so that the faster-traveling express trains
catch up to slower-traveling local trains at express stations only;
at those express stations, the express trains are permitted to pass
local trains.
[0102] FIGS. 4a through 4e illustrate an example of express subway
station E.sub.x on subway line SLINE constructed according to one
embodiment of the invention in which passenger transfers occur at a
location beyond the station platform. FIG. 4a is a plan view of
express station E.sub.x, at which eastbound and westbound platforms
50e, 50w, respectively, are provided for passenger boarding and
de-boarding. Main track 52e for eastbound trains and main track 52w
for westbound trains pass between platforms 50e, 50w, and are
adjacent to their respective platforms 50e, 50w. Side track 54e is
provided adjacent to main track 52e at the location of station
E.sub.x, and abuts the end of platform 50e as shown; side track 54e
couples to main track 52e in both directions, as shown, under the
control of conventional switches (not shown). Similarly, side track
54w is provided adjacent to main track 52w at station E.sub.x,
abutting the end of platform 50w; side track 54w also couples to
main track 52w in both directions.
[0103] FIG. 4b illustrates station E.sub.x in operation, according
to this embodiment of the invention, at a time that eastbound local
train LOC.sub.0 and eastbound express train EXP.sub.0 are stopped
at station E.sub.x. In this example, local train LOC.sub.0 arrived
at station Ex before express train EXP.sub.0, considering that the
effective travel velocity of express train EXP.sub.0 is faster than
that of local train LOC.sub.0 according to embodiments of this
invention, as described above. Earlier-arriving local train
LOC.sub.0 has pulled onto side-track 54e at station E.sub.x, and
has backed up (westward) by a small distance so that its trailing
end is at or near the end of platform 50e (FIG. 4c illustrates an
expanded view of this area of express station E.sub.x with local
train LOC.sub.0 and express train EXP.sub.0 stopped thereat).
Meanwhile, the later-arriving express train EXP.sub.0 has stopped
at station E.sub.x, but remains on main track 52e; as will be
evident from this description, express train EXP.sub.0 will depart
station Ex on main track 52e ahead of local train LOC.sub.0, to
effect its pass of local train LOC.sub.0 along subway line
SLINE.
[0104] As shown in FIG. 4b, express train EXP.sub.0 in this example
is twice as long than local train LOC.sub.0. More specifically,
express train EXP.sub.0 has a front half EXP.sub.0,F that is about
the length of local train LOC.sub.0, and a rear half EXP.sub.0,R.
At the time that both express train EXP.sub.0 and local train
LOC.sub.0 are stopped at express station E.sub.x, front half
EXP.sub.0,F is stopped adjacent to local train LOC.sub.0, and rear
half EXP.sub.0,R is stopped adjacent to platform 50e. FIG. 4c
illustrates this position of trains EXP.sub.0, LOC.sub.0, and
platform 50e in further detail. Local train LOC.sub.0 consists of n
coupled cars, with the rear-most car LOC.sub.0(n) abutting platform
50e, and cars LOC.sub.0(n-1), LOC.sub.0(n-2), etc. in sequence
ahead of rear-most car LOC.sub.0(n). Similarly, front half
EXP.sub.0,F of express train EXP.sub.0 consists of m coupled cars,
with the rear-most car EXP.sub.0,F(m) stopped adjacent to local
train car LOC.sub.0(n), and cars EXP.sub.0,F(m-1),
EXP.sub.0,F(m-2), etc. in sequence ahead of rear-most car
EXP.sub.0(m) and adjacent to corresponding cars LOC.sub.0(n-1),
LOC.sub.0(n-2), etc. of local train LOC.sub.0. Rear half
EXP.sub.0,R of express train EXP.sub.0 is stopped adjacent to
platform 50e, as described above, with its front-most car
EXP.sub.0,R(1) shown in FIG. 4c. Trailing cars EXP.sub.0,R(1) et
seq. (not shown) are coupled in sequence behind front-most car
EXP.sub.0,R(1) to complete rear half EXP.sub.0,R. Front-most car
EXP.sub.0,R(1) is also coupled to the trailing end of rear-most car
EXP.sub.0,F(m), to keep front half EXP.sub.0,F and a rear half
EXP.sub.0,R as a unitary express train EXP.sub.0.
[0105] As shown in FIG. 4d, according to this embodiment of the
invention, distance D.sub.st between main track 52e and its side
track 54e (shown center-line to center-line in FIGS. 4b and 4d) is
selected so that adjacent cars of local train LOC.sub.0 and express
train EXP.sub.0, when both are stopped at station E.sub.x, are
sufficiently close together to allow passengers to transfer
directly between the two trains LOC.sub.0, EXP.sub.0. Of course,
side doors of adjacent cars of trains LOC.sub.0, EXP.sub.0 must be
aligned with one another to permit such passenger transfer. FIG. 4c
schematically illustrates the paths of passenger movement between
trains LOC.sub.0, EXP0. Similarly, main track 52e is positioned
sufficiently close to platform 50e that passengers can safely and
easily board and de-board express train EXP.sub.0 when stopped at
the platform, as shown in FIG. 4c with respect to car
EXP.sub.0,R(1).
[0106] FIG. 4d illustrates, by way of an elevation view, that local
train car LOC.sub.0(n) is positioned sufficiently close to adjacent
express train car EXP.sub.0,F(n) that passengers can easily step
over separation distance D.sub.sep between cars LOC.sub.0(n) and
EXP.sub.0,F(n), and vice versa. It is contemplated that separation
distance D.sub.sep is on the order of the distance between platform
50e and cars in express train rear half EXP.sub.0,R. In any event,
this separation distance D.sub.sep is contemplated to be
significantly smaller than separation distance D.sub.trv between
trains passing in opposite directions on main tracks 52, 52w, as
shown in FIG. 4d; that separation distance D.sub.trv is
contemplated to be at least as wide as the minimum specified
separation between passing trains at any point along subway line
SLINE. As evident from FIGS. 4a through 4e, and particularly in
FIG. 4d, side track 54w is positioned relative to main track 52w in
similar fashion as side track 54e is to its main track 52e. FIG. 4e
illustrates the situation of FIG. 4d, in which local trains
LOC.sub.e, LOC.sub.w are stopped on their respective side tracks
54e, 54w, in both directions at the same express station E.sub.x.
As evident from FIG. 4a, side track 54 may be placed either
"uptrack" or "downtrack" from its associated platform 50; of
course, as will become apparent from the following description, the
scheduling and train car assignments generated for subway line
SLINE by system 20 must take into account the position of side
tracks 54 relative to their express stations.
[0107] It is contemplated that the separation distance D.sub.sep
between adjacent trains LOC, EXP on one of main tracks 52 and its
corresponding side track 54 can be significantly smaller than
separation distance D.sub.trv between passing trains on main tracks
52, 54 because the relative speeds with which adjacent trains LOC,
EXP are traveling in the same direction at the locations of side
tracks 54 are at best quite slow. When trains LOC, EXP traveling in
the same direction are adjacent to one another at the location of
side track 54, one of the two trains (typically local train LOC) is
necessarily stopped, and the other train (typically express train
EXP) is either stopping, starting, or completely stopped itse1f. On
the other hand, passing trains on main tracks 52e, 52w may be
traveling at their full speeds when passing by one another, with
their speeds relative to one another amounting to the sum of their
individual instantaneous velocities (as they are passing in
opposite directions). Accordingly, it is contemplated that station
separation distance D.sub.sep can be significantly smaller than
passing separation distance D.sub.trv, enabling passenger transfer
directly from train to train.
[0108] FIGS. 5a through 5e illustrate the operation of subway line
SLINE in connection with stops of express train EXP.sub.0 and local
train LOC.sub.0 at express station E.sub.x of the embodiment of the
invention described above relative to FIGS. 4a through 4e. This
description will assume that passengers on a given train
(especially if the train is crowded) may not necessarily move from
car-to-car within that same train, as is typical in modern subway
trains. As described above, in this embodiment of the invention,
passenger transfer between express train EXP.sub.0 and local train
LOC.sub.0 occurs at a point beyond platform 50e. FIG. 5a
illustrates a first step in the overall process, with eastbound
local train LOC.sub.0 making its stop at express station E.sub.x
along main track 52e, and adjacent eastbound platform 50e.
Passengers board and de-board local train LOC.sub.0 from and to
platform 50e, during the time period illustrated in FIG. 5a.
[0109] After the stop made by local train LOC.sub.0 at platform 50e
in FIG. 5a, local train LOC.sub.0 then proceeds onto side track
54e, and waits on side track 54e, in order to enable a
later-arriving express train EXP.sub.0 to pass at this express
station E. This state of operation is illustrated in FIG. 4b, along
with express train EXP.sub.0 approaching express station E.sub.x
and its platform 50e, on main track 52e. FIG. 5c illustrates the
position of express train EXP.sub.0 as it stops at express station
E.sub.x, specifically with express train front half EXP.sub.0,F
stopped adjacent to local train LOC.sub.0, and express train rear
half EXP.sub.0,R stopped adjacent to platform 50e; FIG. 5c also
illustrates that local train LOC.sub.0 has backed up from its
earlier position shown in FIG. 5b, and now abuts the end of
platform 50e. As mentioned above, the doors of the cars of express
train front half EXP.sub.0,F should be aligned with doors of the
cars of local train LOC.sub.0 at this stage of operation. Passenger
transfer between express train front half EXP.sub.0,F and local
train LOC.sub.0, and between platform 50e and express train rear
half EXP.sub.0,R, then takes place in the stage of operation
illustrated in FIG. 5c. Insofar as express train EXP.sub.0 is
concerned, the effective length of the platform, as established by
the combination of platform 50e and local train LOC.sub.0, is twice
that of platform 50e itself.
[0110] It is useful at this point to consider the various
passengers on board trains LOC.sub.0, EXP.sub.0 and other trains
along subway line SLINE, with respect to their respective trips.
Those passengers that board at a local station, remain on a local
train throughout their trip, and exit at a local station will be
referred to in this specification as "LLL" passengers (i.e.,
"local-local-local" passengers). Similarly, those passengers that
board at an express station, remain on an express train throughout
their trip, and exit at an express station will be referred to
herein as "EEE" passengers (i.e., "express-express-express"
passengers). In these embodiments of the invention in connection
with side-by-side transfer, neither of the EEE or LLL passengers
need make a transfer. Some passengers, however, will wish to take
advantage of express train service even though embarking or
disembarking at a local-only station. Those passengers who board at
a local station, transfer at some point to an express train during
their trip, and de-board at a local station, will be referred to
herein as "LEL" passengers (i.e., "local-express-local"
passengers). Other combinations are also possible, such as those
passengers who board at an express station, travel at least one
interval on an express train, but exit at a local station; these
passengers will be referred to herein as "EEL" passengers (i.e.,
"express-express-local" passengers). "LEE" passengers of course
board at a local station, transfer to an express train, and exit at
an express station.
[0111] Referring again to FIG. 5c, the EEE and LLL passengers will
of course remain on their respective trains EXP.sub.0, LOC.sub.0
during the stop and transfer operation. Those LEL or EEL passengers
currently on express train EXP.sub.0 and for whom express station
E.sub.x is the last express station along subway line SLINE before
their local destination station should transfer from express train
EXP.sub.0 to local train LOC.sub.0 while trains EXP.sub.0,
LOC.sub.0 are in the position of FIG. 5c. Similarly, LEL and LEE
passengers currently on local train LOC.sub.0 should transfer to
express train EXP.sub.0 during the time that trains EXP.sub.0,
LOC.sub.0 are in the position of FIG. 5c, and should remain on that
until their destination express station (for LEE passengers) or
until the last express station before their destination local
station (for LEL passengers). As evident from this description,
every passenger can travel along subway line SLINE according to
this embodiment of the invention without setting foot on any
platform 50 other than at their ultimate starting and destination
stations.
[0112] Once passenger transfer is completed, then express train
EXP.sub.0 is allowed to leave express station E.sub.x via main
track 52e, while local train LOC.sub.0 remains stopped on side
track 54e. This operation is illustrated in FIG. 5d, which shows
express train rear half EXP.sub.0,R leaving express station E.sub.x
on main track 52e (on which it has remained throughout the process
of the stop at express station E.sub.x). In this way,
later-arriving express train EXP.sub.0 physically passes local
train LOC.sub.0, which arrived at express station E.sub.x before
express train EXP.sub.0 but is leaving express station E.sub.x
later. After express train EXP.sub.0 has left express station
E.sub.x, then local train LOC.sub.0 leaves express station E.sub.x
by traveling from side track 54e to main track 52e, as shown in
FIG. 5e.
[0113] As evident from FIGS. 4b, 4c, and 5c, simultaneous transfer
of passengers between trains LOC.sub.0, EXP.sub.0 directly, and
between express train EXP.sub.0 and platform 50e is enabled by the
use of an express train EXP.sub.0 with greater length than its
corresponding local train LOC.sub.0. In one example of the
operation of subway line SLINE according to this embodiment of the
invention, for passenger safety, inter-car transfer within the same
train is not permitted, nor are passengers permitted to transfer
between platform 50e and local train car LOC.sub.0(n) in the
situation shown in FIGS. 4c and 5c. As such, at express station
E.sub.x of FIGS. 4a through 4e and 5a through 5e, passengers
boarding express train EXP.sub.0 from platform 50e (such passengers
preferably of the EEE types in this embodiment of the invention)
can only board cars in express train rear half EXP.sub.0,R;
meanwhile, passengers transferring between express train EXP.sub.0
local train LOC.sub.0, in either direction, can only do so relative
to express train front half EXP.sub.0,F. As such, only those
passengers riding in express train front half EXP.sub.0,F can
transfer to local train LOC.sub.0 (and thus de-board at one of the
upcoming local stops) over the express interval I.sub.x beginning
with express station E. Passengers riding in express train rear
half EXP.sub.0,R must remain on express train EXP.sub.0 until at
least the next express station E.sub.x+1 in this example.
Passengers boarding at express station E.sub.x but whose
destination is a local station (i.e., EEL passengers) should board
local train LOC.sub.0 when it arrives at platform 50e (FIG. 5a) and
then transfer to express train EXP.sub.0 during a side-by-side
transfer as shown in FIG. 5c.
[0114] It is contemplated that the schedule generated by system 20
for local and express trains along subway line SLINE will in some
way comprehend this limitation relative to the boarding and
de-boarding of express trains EXP.sub.0, and transfers to and from
local trains LOC. Of course, express trains EXP stopping at express
station E.sub.x may make two short stops: one stop with express
train front half EXP.sub.0,F at platform 50e, and the second stop
with express train rear half EXP.sub.0,R at platform 50e (indeed,
one can contemplate a third stop, with express train rear half
EXP.sub.0,R adjacent local train LOC.sub.0). However, it is
contemplated that such multiple stops by express trains at each
express station will add to the overall passenger travel time for
both express and local passengers (especially considering that this
additional time will occur at every express station), and is
therefore disfavored.
[0115] Referring now to FIGS. 5f and 5g, the operation of this
embodiment of the invention in connection with express train
EXP.sub.0 of the same length of local train LOC.sub.0, and thus of
about the same length as platform 50e at which it is making a stop,
will now be described. In FIG. 5f, local train LOC.sub.0 is
positioned on side track 54e; prior to the point in time shown in
FIG. 5f, local train LOC.sub.0 had already stopped at platform 50e
to allow passengers to board and de-board, following which it
proceeded down main track 52e and then backed into side track 54e.
At the point in time shown in FIG. 5f, express train EXP.sub.0 has
arrived at express station E.sub.x, and is aligned with platform
50e to permit passengers to board and de-board (e.g., EEE and LEE
passengers).
[0116] The approach shown in FIG. 5f provides the ability for
express train EXP.sub.0 to physically pass earlier arriving local
train LOC.sub.0 at an express station E.sub.x that has a reduced
footprint. However, the passing process in that embodiment of the
invention requires express train EXP.sub.0 to make two full
stops--one at platform 50e to permit passengers to board and
deboard express train EXP.sub.0 from and to express station
E.sub.x, and another stop adjacent to local train LOC.sub.0 to
permit EEL passengers to transfer from express train EXP.sub.0 to
local train LOC.sub.0. According to an alternative approach shown
in FIG. 5g, express train EXP.sub.0 can accomplish the necessary
passenger movements in a single stop. At the point in time shown in
FIG. 5g, express train EXP.sub.0 makes its stop at express station
E.sub.x at a position that is half-aligned with platform 50e and
half-aligned with local train LOC.sub.0. This stop position allows
passengers to board and deboard the rear half of express train
EXP.sub.0 from and to express station E.sub.x, and simultaneously
allows direct train-to-train passenger transfers between trains
LOC.sub.0 and EXP.sub.0. More specifically, EEE passengers will
board the rear half of express train EXP.sub.0. LEE passengers, who
previously de-boarded local train LOC.sub.0 at its stop at platform
50e, will also board the rear half of express train EXP.sub.0;
these LEE passengers will have been instructed or restricted to
have boarded the front half of local train LOC.sub.0 at their
station of origin, and will have been instructed to de-board local
train LOC.sub.0 at platform 50e. Those LEL passengers who are
transferring to express train EXP.sub.0 for the express portion of
their journey over the next express interval will have been
instructed to have boarded the rear half of local train LOC.sub.0
at their station of origin, so that they can make the direct
transfer to the front half of express train EXP.sub.0 at this time.
Therefore, at the point in time shown in FIG. 5g, these LEL
passengers on the rear half of local train LOC.sub.0 can transfer
directly to the front half of express train EXP.sub.0 to begin the
express portion of their journey, and LEL and EEL passengers
already on the front half of express train EXP.sub.0 can transfer
directly to the rear half of local train LOC.sub.0 to begin the
final local portion of their journey. Following this direct
transfer opportunity, express train EXP.sub.0 leaves express
station E.sub.x first, followed by local train LOC.sub.0, as
described above relative to FIGS. 5d and 5e.
[0117] According to another embodiment of the invention, side track
56e is located on the "uptrack" side of platform 50e, to facilitate
passenger movement as will now be described relative to FIGS. 5h
and 5i for the case of express train EXP.sub.0 of the same length
as local train LOC.sub.0, and of a length that is about that of
platform 50e. As shown in FIG. 5h, express station E.sub.x has
eastbound platform 50e and westbound platform 50w associated with
eastbound and westbound main track 52e, 52w, respectively.
Platforms 50e, 50w are each associated with a corresponding uptrack
side track 56e, 56w. Side tracks 56e, 56w are uptrack in the sense
that it can receive a train prior to that train arriving at the
corresponding platform 50e, 50w.
[0118] FIG. 5h illustrates the operation of express station E.sub.x
in serving stops for local train LOC.sub.0 and express train
EXP.sub.0 in this embodiment of the invention. At the point in time
shown in FIG. 5h, local train LOC.sub.0 has already arrived at
express station E.sub.x from the west, but rather than stopping at
platform 50e, has pulled into uptrack side track 56e. Express train
EXP.sub.0 has arrived at station E.sub.x later than did local train
LOC.sub.0, and is shown in FIG. 5h in its positioned as stopped at
platform 50e. In this embodiment of the invention, express train
EXP.sub.0 stops with its leading portion at platform 50e, and its
trailing portion aligned with the leading portion of local train
LOC.sub.0. In this position, boarding express passengers (i.e.,
both EEE and EEL passengers) may board express train EXP.sub.0 from
the rear half of platform 50e, and de-boarding express passengers
(i.e., both EEE and LEE passengers) may de-board express train
EXP.sub.0 to platform 50e. Meanwhile, passengers (e.g., EEL, LEL
passengers) may transfer directly from the rear half of express
train EXP.sub.0 to local train LOC.sub.0, and passengers (e.g.,
LEL, LEE passengers) may transfer directly from the front half of
local train LOC.sub.0 to express train EXP.sub.0, in the manner
described above relative to FIG. 4d. Following this stop, express
train EXP.sub.0 may then directly leave platform 50e and express
station E.sub.x via main track 52e, continuing its express service
along subway line SLINE, as shown in FIG. 5i. In FIG. 5i, local
train LOC.sub.0 has moved forward, via spur 56', to stop at
platform 50e. At this time, LEE passengers who previously
transferred to local train LOC.sub.0 from the rear half of express
train EXP.sub.0 (FIG. 5h) may then de-board local train LOC.sub.0
to platform 50e. EEL passengers who previously de-boarded from the
front half of express train EXP.sub.0 may then re-board local train
LOC.sub.0 for the local leg of their journey to the desired local
destination station along the next interval.
[0119] In this embodiment of the invention, the efficiency of the
stop at express station E.sub.x for local train LOC.sub.0 is
improved relative to that described above in connection with FIGS.
4a through 4d, because local train LOC.sub.0 need not back up over
more than its entire length in order to utilize side track 56e;
rather, local train LOC.sub.0 need only back up a short distance
away from platform 50e along side track 56e, before moving forward
again via spur 56' to main track 52e and platform 50e. The
efficiency of the stop for express train EXP.sub.0 is also
improved, because express train EXP.sub.0 need only make one stop
rather than two. Those passengers in the rear half of express train
EXP.sub.0 can de-board at platform 50e by first transferring to
local train LOC.sub.0 (FIG. 5h), and then de-boarding local train
LOC.sub.0 when it stops at platform 50e (FIG. 5i). Passengers who
wish to transfer from the front part of express train EXP.sub.0 may
also perform a two-step transfer, from express train EXP.sub.0 to
platform 50e and then from platform 50e to local train
LOC.sub.0.
[0120] In summary, the operation of express station E.sub.x shown
in FIGS. 5h and 5i is less restrictive than that shown in FIG. 5g.
More specifically, the entire length of express train EXP.sub.0 has
access, either direct or indirect, to platform 50e and the entire
length of local train LOC.sub.0; the front half of local train
LOC.sub.0 also has access to both platform 50e and express train
EXP.sub.0. Passengers already in the rear half of local train
LOC.sub.0 are still partially restricted, in that they cannot
transfer to express train EXP.sub.0; it is contemplated, however,
that passengers can be instructed by system 20, at their station of
origin, to board the front half of local train LOC.sub.0 if they
intend to transfer an express train. The rear half of local train
LOC.sub.0 can receive EEL and LEL passengers from express train
EXP.sub.0 indirectly, at its stop at platform 50e at the point in
time shown in FIG. 5i.
[0121] FIGS. 5j and 5k illustrate the operation of the eastbound
side of express station E.sub.x with uptrack side track 56e in the
case in which express train EXP.sub.0 is of twice the length of
local train LOC.sub.0 and of platform 50e. In the state of
operation shown in FIG. 5j, local train LOC.sub.0 has already
arrived at express station E.sub.x, and has pulled into side track
56e before stopping at platform 50e. Later, express train EXP.sub.0
has arrived at express station E.sub.x, and is stopped with its
front half EXP.sub.0,F at platform 50e and its rear half
EXP.sub.0,R aligned with local train LOC.sub.0. Passengers may
board and de-board express train front half EXP.sub.0,F from and to
platform 50e at this time, and passengers may transfer directly
between local train LOC.sub.0 and express train rear half
EXP.sub.0,R in the manner described above relative to FIG. 4d.
Express train EXP.sub.0 can then leave express station E.sub.x
after this single stop.
[0122] In FIG. 5k, express train EXP.sub.0 has left express station
E.sub.x, and local train LOC.sub.0 has backed up slightly, and then
moved forward via spur 56' to stop at platform 50e. As before,
passengers may now board local train LOC.sub.0 from platform 50e,
and other passengers may de-board local train LOC.sub.0 to platform
50e (including those passengers who transferred to local train
LOC.sub.0 from express train rear half EXP.sub.0,R during the stop
shown in FIG. 5j). As a result, each of local train LOC.sub.0 and
express train EXP.sub.0 need make only a single stop at express
station E.sub.x, while permitting full flexibility in the movement
of passengers between trains LOC.sub.0, EXP.sub.0.
[0123] This operation of subway line SLINE according to these
embodiments of this invention can be further described in
connection with the schematic views of subway line SLINE shown in
FIGS. 5l through 5o. Similarly as in the case of FIGS. 3e through
3h, FIGS. 5l through 5o are plan views of subway line SLINE from
above (and through the earth above subway line SLINE) at particular
points in time. FIG. 5l illustrates the state of subway line SLINE
at a point in time in which express train {circumflex over (T)}6 is
beginning the trip along subway line SLINE, at express station E0,
just ahead of local train T12; meanwhile, at this point, express
trains {circumflex over (T)}5, {circumflex over (T)}4, and
{circumflex over (T)}3 have caught up to their respective local
trains T10, T8, T6 at express stations E1, E2, E3, respectively. As
such, according to embodiments of this invention described above in
connection with FIGS. 4a through 4d and 5a through 5i, express
trains {circumflex over (T)}5, {circumflex over (T)}4, and
{circumflex over (T)}3 physically pass their respective local
trains T10, T8, T6; FIG. 5m illustrates subway line SLINE at this
point in time after this physical passing operation. As described
above, these physical pass operations also involve passenger
boarding, de-boarding, and transfer. FIG. 5n illustrates the state
of subway line SLINE at a time during the next express interval, in
which express trains {circumflex over (T)}6, {circumflex over
(T)}5, {circumflex over (T)}4, and {circumflex over (T)}3 are
traveling along subway line SLINE ahead of the local trains T12,
T10, T8, T6 that they recently passed. However, each of these
express trains {circumflex over (T)}6, {circumflex over (T)}5,
{circumflex over (T)}4, and {circumflex over (T)}3 are catching up
to the local trains T11, T9, T7 etc. that are ahead along subway
line SLINE, as shown in FIG. 5n. And, as shown in FIG. 5o, express
trains {circumflex over (T)}6, {circumflex over (T)}5, and
{circumflex over (T)}4, catch up to respective local trains T11,
T9, T7, at the next express station E1, E2, E3, respectively. At
that time, as shown in FIG. 5o, the next express train {circumflex
over (T)}7 is sent along subway line SLINE from origin station E0,
ahead of the next local train T13. Of course, in the same manner as
shown in FIG. 5m, express trains {circumflex over (T)}6,
{circumflex over (T)}5, and {circumflex over (T)}4 will physically
pass these respective local trains T11, T9, and T7 in the manner
described above, in connection with FIGS. 4a through 4d and 5a
through 5i, continuing the process.
[0124] According to each of these embodiments of the invention,
therefore, express train EXP.sub.0 can physically pass local train
LOC.sub.0 at express station E.sub.x, thus enabling express service
over a single track on which local trains also operate. While
flexibility in passenger movement is provided by these embodiments
of the invention, it is useful for system 20 to assist passengers
by way of at-station and on-train graphics displays instructing
passengers regarding the portion of the train that they ought to
board in order to carry out their desired transfers to and from
express trains, for example in order to optimize travel to a
particular destination station. It may be useful that such
at-station and on-train displays illustrate visualizations of the
entirety of subway line SLINE to show the approach and passing of
local trains by express trains, to assist passenger understanding
of this operation. Alternatively, or in addition, system 20 may
also provide transfer and car assignment instructions in connection
with point-to-point ticketing.
[0125] As evident in each of these embodiments of the invention,
express station E.sub.x is no wider (i.e., in the direction
perpendicular to tracks 52) due to the presence of side tracks 54e
or 56e, than that which is otherwise necessary to provide main
tracks 52e, 52w and platforms 50e, 50w without side tracks.
Accordingly, existing subway lines may be retrofitted by
construction of side tracks 54 at its express stations, with much
reduced excavation and construction costs than would be required to
include conventional side tracks on opposite sides of the platform
(as described above relative to FIG. 1). It is therefore
contemplated that, in many existing subway systems, the provision
of express subway service over two-track subway lines is rendered
feasible by this embodiment of the invention.
[0126] Local to Express Train "Transformation"
[0127] According to another embodiment of this invention, express
and local subway trains traveling along the same two-track subway
line SLINE are scheduled and operated to meet at express stations
only, similarly as in the embodiments described above in which
express trains physically pass the earlier-arriving local trains.
According to this embodiment of the invention, however, express
trains can be considered to "virtually" pass the local trains. This
is accomplished by transforming individual trains from providing
express service to providing local service, and vice versa, at
express stations. In other words, the same physical train that
provides local service over one interval between express stations
is transformed to provide express service over the next interval
between express stations; conversely, the same physical train that
provides express service over one interval between express stations
may be transformed to provide local service over the next interval
between express stations.
[0128] In a general sense, according to this embodiment of the
invention, a group of n trains (n.gtoreq.2) traveling in the same
direction arrive simultaneously at an express station along the
two-track subway line SLINE. In this case, the earliest arriving
train (or trains) will have been providing local service over the
previous interval between express stations, and later arriving
trains will have been providing express service over that interval,
catching up to the local train at the express station according to
the schedule. According to this embodiment of the invention, the
last one or more of the express trains arriving at this express
station (which, given the above description, mean the last one or
more of the trains in this group of trains) provide local service
over the next interval between express stations. The earliest
arriving train (formerly providing local service) and perhaps one
or more of the next-to-arrive trains at this express station
provide express service over the next interval between express
stations. Because of this transformation, the train that is
providing local service is no longer at the head of the group of
trains, but is at the tail--this local service train will not hold
up the progress of the express trains that are now in front of it
along subway line SLINE.
[0129] FIG. 6 illustrates this scheduling and operation of trains
according to this embodiment of the invention, by way of a travel
diagram. In this example, three trains TRN.sub.1, TRN.sub.2,
TRN.sub.3 are traveling in the same direction along a two-track
subway line SLINE, and are traveling from express station E0 to
express station E3. It is contemplated that this operation of
subway line SLINE in a manner according to this embodiment of the
invention may be based on a schedule created by a computer system,
such as system 20 described above relative to FIG. 3a, for example
as generated and modified by way of the process described above
relative to FIG. 3b. In addition, it is contemplated that system 20
can also monitor the real-time operation of trains along subway
line SLINE, and control or suggest the operation of trains (e.g.,
by way of instantaneous travel velocity, or delays at particular
stations, and the like) to minimized wait times and other
non-productive delays. As described above, the scheduling of trains
TRN.sub.1 et seq. is performed with a goal of express trains
catching up to local trains only at express stations, thus
minimizing the time and distance over which the travel velocity of
a subway train providing express service is limited by a local
subway train traveling ahead of it along the same track.
[0130] As evident from FIG. 6, according to this embodiment of the
invention, express trains travel at an effective travel velocity
V.sub.exp; at that express velocity V.sub.exp, a train may travel
from one express station to the next (e.g., from station E0 to
station E1) within one time interval (time t1 to time t2). Local
trains travel at an effective travel velocity V.sub.loc, which in
the example of FIG. 6 is one-half of express velocity V.sub.exp. As
such, a train traveling at local velocity V.sub.loc requires two
time intervals (e.g., time t0 to time t2) to travel from one
express station to the next (station E0 to station E1). As
discussed above, the slower effective travel velocity V.sub.loc for
trains providing local subway service need not necessarily result
from a slower instantaneous velocity, but may instead result from
the intermediate stops made at local stations along the interval
between express stations.
[0131] In the example of FIG. 6, and according to this embodiment
of the invention, train TRN.sub.1 leaves express station E0 at time
t1. Train TRN.sub.1 provides local service over the interval
between express stations E0 and E1, travelling at local travel
velocity V.sub.loc, until reaching express station E1 at time t3.
Train TRN.sub.2 leaves express station E0 at a later time t2, but
travels at express travel velocity V.sub.exp so that it also
arrives at express station E1 at time t3. However, because train
TRN.sub.1 left station E0 immediately before train TRN.sub.2, train
TRN.sub.1 occupies a position on two-track subway line SLINE ahead
of train TRN.sub.2, and thus arrives at express station E1 ahead of
(but essentially simultaneously with) train TRN.sub.2. According to
this embodiment of the invention, train TRN.sub.1 "transforms" into
an express train at express station E1, and as such travels at
express velocity V.sub.exp over the interval between express
stations E1 and E2. Conversely, train TRN.sub.2 transforms into a
local train at express station E1 to provide local service over the
interval between express stations E1 and E2, travelling at local
velocity V.sub.loc. Because local velocity V.sub.loc is slower than
express velocity V.sub.exp, train TRN.sub.2 falls behind train
TRN.sub.1 over this interval; conversely, train TRN.sub.1 is not
held up by a slower-moving local train ahead of it on the track (at
least until reaching express station E2 at time t4, at which time
it catches up to a local train, if any, that is ahead of it on the
track).
[0132] Meanwhile, train TRN.sub.3 leaves express station E0 at time
t2, at which point it provides local service over the interval
between stations E0 and E1. In doing so, train TRN.sub.3 travels at
the slower local effective travel velocity V.sub.loc, arriving at
express station E1 at time t4, one time interval after train
TRN.sub.2 arrived at express station E1. Over the next interval,
between stations E1 and E2, train TRN.sub.3 transforms into an
express train, traveling at express travel velocity V.sub.exp, and
arriving at express station E2 at time t5. Meanwhile, train
TRN.sub.2 has provided local service, at effective local travel
velocity V.sub.loc, between express stations E1 and E2, reaching
the next express station E2 at time t5. Because train TRN.sub.2 is
ahead of train TRN.sub.3 on the track, train TRN.sub.3 essentially
catches up to train TRN.sub.2 at express station E2, but cannot
physically pass train TRN.sub.2. Instead, according to this
embodiment of the invention, train TRN.sub.2 transforms into an
express train at station E2, traveling at express travel velocity
V.sub.exp over the interval between express stations E2 and E3;
train TRN.sub.3 transforms into a local train at station E2,
providing local service over the interval between express stations
E2 and E3 and traveling at local travel velocity V.sub.loc.
[0133] The operation of trains TRN.sub.1, TRN.sub.2, TRN.sub.3
continues in this manner, along with those trains ahead of and
following after these trains along subway line SLINE. In this
example, each train traveling along two-track subway line SLINE
alternates between providing local service and providing express
service, from express interval to express interval. In effect,
therefore, each train operates at a higher average travel velocity
over the entire length of subway line SLINE, considering that each
train does not make local stops over alternating express intervals
(and may also travel at higher instantaneous velocities over those
intervals, depending on the schedule and operator). The schedule
generated and operated by the subway operator, for example through
the use of system 20 and the process of FIG. 3b, optimizes
efficiency of this operation by limiting the time that the faster
moving express trains are held up by the slower traveling local
trains.
[0134] In the example of FIG. 6, trains TRN.sub.1 through TRN.sub.3
are effectively transforming at each express station as a group of
two--each train and the train immediately ahead of it or behind it
at the express station, as the case may be. FIG. 7a illustrates
this operation of two-train groups in further detail, relative to
four trains T1 through T4 proceeding in sequence in the same
direction along two-track subway line SLINE. In the example of FIG.
7a, stop times at the various stations are ignored, for clarity of
the description.
[0135] As shown in FIG. 7a, trains T2 and T3 arrive at and leave
express station E0 at time t=10 minutes, with train T2 providing
express service from express station E0 and train T3 providing
local service from express station E0. In this example, train T2 in
its express mode arrives at express station E1 at time t=15
minutes, while at that same time, train T3 arrives at local station
L1 between express stations E0 and E1. Meanwhile, train T1 has been
providing local service between express stations E0 and E1, leaving
express station E0 at time t=5 minutes, stopping at local station
L1 at time t=10 minutes, and arriving at express station E1 just
ahead of train T2 at time t=15 minutes. As such, at time t=15
minutes, both of trains T1 and T2 are at express station E1, with
train T1 ahead of train T3 along two-track subway line SLINE.
[0136] According to this embodiment of the invention, at express
station E1 at time t=15 minutes, train T1 transforms from a local
train into an express strain and train T2 transforms from an
express train into a local train. As such, train T1 provides
express service from express station E1, arriving at express
station E2 at time t=20 minutes, and train T2 provides local
service from express station E1, arriving at local station L2 at
time t=20 minutes. Meanwhile, train T3 arrives at express station
E1 at time t=20 minutes, having provided local service between
express stations E0 and E1, immediately followed by train T4 which
has been providing express service between express stations E0 and
E1. Train T3 transforms into providing express service from express
station E1, beginning at time t=20 minutes, and arrives at express
station E2 at time t=25 minutes, immediately after train T2, which
continued its local service from local station L2 until reaching
express station E2 at that same time, but ahead of train T3. From
this point forward, the sequence of operations essentially repeats
(i.e., the status of trains T1, T2, T3 at time t=25 minutes matches
that at time t=10 minutes).
[0137] This process of alternating between providing express
service and providing local services continues over time, along
two-track subway line SLINE, in this two-train group example. Each
train alternates between providing express and local service in
this manner, meeting up with the trains immediately ahead and
behind at each express station, in the manner described above. As a
result, each train travels at the higher effective express velocity
(V.sub.exp) for half of the express intervals, and at the slower
effective local velocity (V.sub.loc) for the other half of the
express intervals. If the express intervals are of equal length,
and if local velocity V.sub.loc is one-half that of express
velocity V.sub.exp, then operation according to this two-train
group approach provides a 25% reduction in the passenger travel
time over subway line SLINE.
[0138] According to this embodiment of the invention, trains may
transform according to more than two trains per "group". FIG. 7b
illustrates the operation of subway line SLINE for the example of
three-train groups, in which the last train in a given group
leaving an express station provides local service over the express
interval and the first two trains provide express service over that
interval. For example, three trains T5, T6, T7 leave express
station E0 at time t=15 minutes, in FIG. 7b. Train T7 provides
local service from express station E0, arriving at local station L1
at time t=20 minutes; meanwhile, trains T5 and T6 provide express
service from express station E0, arriving at express station E1 at
time t=20 minutes. At that time t=20 minutes and at express station
E1, trains T5 and T6 catch up to train T4, but remain behind train
T4 along subway line SLINE. Over the express interval from express
station E1, trains T4 and T5 provide express service, while
trailing train T6 provides local service from express station E1,
stopping at local station L2 at time t=25 minutes. Trains T4 and T5
arrive at the next express station E2 at time t=25 minutes.
[0139] Train T7, which provided local service from express station
E0, arrives at express station E1 at time t=25 minutes. Trains T8
and T9, which provided express service from express station E0,
also arrive at express station E1 at that time, but remain behind
train T7 on subway line SLINE. From express station E1, trains T7
and T8 provide express service, while trailing train T9 provides
local service, stopping at local station L2 at time t=30 minutes,
which in this example is the same time that trains T7 and T8 arrive
at express station E2. Train T6, which provided local service from
express station E1, also arrives at express station E2 at time t=30
minutes, at which time it transforms into providing express service
along with train T7; train T8 provides local service from express
station E2. The process continues in this manner, as shown in FIG.
7b for these three-train groups, with trains T5, T6, T7 finally
catching up to one another, as a group, at express station E3 at
time t=35 minutes, from which point the process repeats in the same
manner.
[0140] In this example, each train travels at the effective express
travel velocity V.sub.exp for two out of every three express
intervals, and travels at the effective local travel velocity
V.sub.loc over the third of those intervals. Under the assumptions
of express intervals of equal length, and local velocity V.sub.loc
one-half that of express velocity V.sub.exp, then operation
according to this three-train group approach provides a 33%
reduction in the passenger travel time over the length of subway
line SLINE.
[0141] FIG. 7c illustrates the operation of subway line SLINE for
the example in which the trains meet at express stations in groups
of four, with the trailing train of that group providing local
service over the next interval from express station. In this
example, we will follow the group of four trains T6, T7, T8, T9,
which leave express station E0 at time t=15 minutes. The trailing
train T9 in this group provides local service over the interval
from express station E0, stopping at local station L1 at time t=20
minutes, while trains T6, T7, T8 provide express service over that
interval, arriving at express station E1 at time t=20 minutes.
Train T5, having provided local service from express station E0,
has arrived at express station E1 immediately prior to trains T6,
T7, T8, at time t=20 minutes. As such, from the group of trains T5,
T6, T7, T8 at express station E1 at time t=20 minutes, train T8 is
the rear-most train of the group and thus will provide local
service over the interval from express station E1, arriving at
local station L2 at time t=25 minutes. Trains T5, T6, T7 all
provide express service over this interval, arriving at express
station E2 at time t=25 minutes, immediately after train T4.
Meanwhile, train T9 continues at its local velocity, and arrives at
express station E1 at time t=25 minutes.
[0142] This operation of trains T6, T7, T8, T9 and the other trains
traveling along subway line SLINE at this time continues in this
fashion. From time t=25, train T8 continues to provide local
service and train T7 begins providing local service (from express
station E2); meanwhile, trains T6 and T9 provide express service
over their respective intervals. Eventually, at time t=40 minutes,
the original group of four trains T6, T7, T8, T9 that we followed
above from express station E0 arrive together again at express
station E4, at time t=40 minutes, from which point the process
repeats again, continuing over the length of subway line SLINE.
[0143] In this example, one train in every group of four trains is
providing local service over an interval between express stations,
while the other three trains are providing express service. With
respect to a single train, each train operates at effective local
travel velocity V.sub.loc over every fourth interval between
express stations, and operates at the effective express travel
velocity V.sub.exp over the other three intervals in that group of
intervals. Under the assumptions of express intervals of equal
length, and local velocity V.sub.loc one-half that of express
velocity V.sub.exp, then operation according to this three-train
group approach provides nearly a 40% reduction in the passenger
travel time over the length of subway line SLINE.
[0144] In particular, it can be appreciated that the density of
trains per unit distance along subway line SLINE can greatly
decrease, for a given passenger throughput rate, through use of
embodiments of this invention. FIGS. 7d through 7g illustrate this
effect, in the form of satellite "snapshots" of the status of
subway line SLINE at various points in time. The snapshots of FIGS.
7d through 7f illustrate the status of subway line SLINE at the
same point in time (i.e., that point in time at which train T0 has
reached express station E6) relative to one another, but for
different train densities along subway line SLINE, as will now be
described.
[0145] FIG. 7d illustrates a portion of subway line SLINE between
express stations E0 and E6 in its conventional operation, in which
every train operates as a local train. The distance intervals
between the various express stations E0 through E6 are shown as
uniform, for the sake of clarity; as discussed above, of course,
this uniform interval is not a requirement in embodiments of this
invention. In the case shown in FIG. 7d, trains T0 through T12
operate in single train "groups"; each train T0 through T12 is
providing only local service. Trains T0 through T12 are spaced in
time from one another, and all of trains T0 through T12 operate at
the same average travel velocity as one another. While express
stations E0 through E6 are shown in FIG. 7d, those stations are
functionally indistinct from one another and from any other station
along subway line SLINE, as there is no express service and thus
each station serves as a local station. In the case shown in FIG.
7d, the density of trains per unit express interval is two.
[0146] FIG. 7e shows subway line SLINE at a similar instant in time
as that of FIG. 7d, but shows the case in which each train
alternates between providing express service and local service.
This corresponds to the two-train groups described above relative
to FIG. 7a. In FIG. 7e, those trains indicated with the " "
character (i.e., trains T1, T4, T7, T10, T13, T16, T19) are
currently providing express service, and are shown in the order as
arriving at the various express stations E0 through E6 (i.e.,
before making a physical or virtual pass of their corresponding
local train also at that station). For example, at express station
E1 in FIG. 7e, train T15 is the first to arrive and has been
providing local service over the previous interval; train T16 will
be next to arrive, and has been providing express service over the
previous interval; as described above, train T15 will then provide
express service over the next interval, and train T16 will provide
local service over that next interval. Because one out of every
three trains on a given express interval of subway line SLINE is
providing express service, at essentially twice the average travel
velocity along the length of subway line SLINE, three trains are
capable of providing the same passenger throughput according to
this invention that would require four local-only trains in the
conventional local-only subway system as shown in FIG. 7d. Not only
do embodiments of this invention thus provide greater efficiency in
train and fuel utilization than does the local-only service, but as
many as one-half of the passengers (on the average) will experience
a significantly shorter travel time. In the case shown in FIG. 7e,
the density of trains per express interval is three (rather than
two in the case of FIG. 7d). But the passenger throughput capacity
of the case of FIG. 7e is twice that of the case of FIG. 7d, and
indeed is equivalent to the throughput capacity of a density of
four local-only trains.
[0147] As described above, the subway operator can increase the
density of trains to take further advantage of the improvement in
efficiency, assuming that additional passenger demand is available.
The snapshot of subway line SLINE shown in FIG. 7f illustrates the
three-train group operation described above relative to FIG. 7b, in
which two trains of every four are providing express service over
any given express interval of subway line SLINE. In the case shown
in FIG. 7f, the density of trains per express interval is four.
Because these express trains are traveling at twice the average
travel velocity as the local trains, the arrangement of FIG. 7f is
capable of carrying the same passenger throughput that would
require six local-only trains in the conventional local-only subway
system of FIG. 7d. If supported by the passenger demand, FIG. 7g
illustrates the case in which three of every five trains are
providing express service over each express interval of subway line
SLINE, as described above relative to FIG. 7c in connection with
the four train groups. In the case of FIG. 7g, the density of
trains per express interval is five, and those five trains are
capable of supporting the same passenger throughput that would
require eight local-only trains in the conventional local-only
subway system of FIG. 7d. Again, not only is the train and fuel
utilization improved through use of embodiments of this invention,
but increasing fractions of passengers will experience shorter
travel times. In some embodiments of this invention, as will be
described below, this shorter travel time is made available to
essentially every passenger.
[0148] Table 1 tabulates, for the trains in a given group, the
intervals over which each train is providing express service and
over which each train provides local service:
TABLE-US-00001 TABLE 1 # of Train position Express Express Express
Express Express Express trains per when leaving interval 1 interval
2 interval 3 interval 4 interval 5 interval 6 FIG. group E0 (E0 to
E1) (E1 to E2) (E2 to E3) (E3 to E4) (E4 to E5) (E5 to E6) 7d 1
Head L L L L L L 7e 2 Head E L E L E L Tail L E L E L E 7f 3 Head E
E L E E L Middle E L E E L E Tail L E E L E E 7g 4 Head E E E L E E
Mid 1 E E L E E E Mid 2 E L E E E L Tail L E E E L E
This Table 1 presumes that only one of the trains in a given group
of trains provides local service, allowing the other trains in that
group to operate at the faster effective express velocity
V.sub.exp. In each case, the last train in any group to leave any
express station will provide local service over the next express
interval; conversely, the first train to leave any express station
will provide express service over the next express interval. In
those cases in which the number of trains within a group is greater
than two, optimum express service is attained by all trains in the
group, except the last to leave the express station, providing
local service over the next interval.
[0149] In each of the cases of FIGS. 7a through 7c described above,
the train providing local service within an express interval serves
as the "pacemaker" for all of the express trains following it
within the interval. The travel time of this local train (e.g.,
train T14 between express stations E1 and E2 in FIG. 7e) is
entirely independent of the number of express trains following it
over that interval. As such, the schedule of local service over the
entirety of subway line SLINE can remain constant, regardless of
the density of trains on that line. This remarkable result enables
the subway operator to vary the number of express trains serving
subway line SLINE over time, for example within the same day (rush
hour vs. non-rush hour), from day to day (weekdays vs. weekends),
or for special events (sporting events, festivals, etc.), without
changing the schedule of the local train service. This ability is
contemplated to greatly facilitate passengers in arranging their
travel, because the frequency and schedule of subway train service
can remain completely fixed, regardless of time of day and day of
the week. The consumer can arrange travel with confidence and ease,
by relying on the local train schedule as a minimum; upon arrival
at the train station, in-station graphics displays or
station-to-station ticketing can advise the passenger of the
availability of any express service at that time. Indeed, it is
contemplated that this consistency in train scheduling will not
only improve customer convenience, but as a result will increase
ridership during off-peak times.
[0150] While the improvement in average train travel velocity
increases as the number of trains per group increases, because a
higher fraction of the trains are traveling at the faster express
velocity V.sub.exp than at the slower local velocity V.sub.loc, the
effective passenger travel time will decrease only if there are a
sufficient number of passengers using the express service to
support the number of express trains assigned. Accordingly, the
selection of the number of trains assigned to each group depends on
the relative passenger demand for express vs. local service. It is
contemplated that system 20 of FIG. 3a, operating according to the
process illustrated in FIG. 3b and described above, will be capable
of deriving the optimum schedule considering these factors of
travel time and passenger demand, and other factors applicable to
subway line SLINE including the available trains, the effects of
stop times at each of the stations, any extraordinary events
occurring along the line that affect operation, and the like. Of
course, subway system management may also have certain operational
constraints that also affect the derivation of the schedule, which
must also be taken into account as appropriate. In any event, it is
contemplated that the operator of subway line SLINE is able to
adjust for the varying volume of passengers at different times of
day, and on different days, by adjusting the number of express
trains assigned. For example, during rush hour, a larger number of
express trains can be used (e.g., as shown in FIGS. 7f and 7g),
while at non-rush hour times or holidays and weekends, fewer trains
may be assigned as express trains (e.g., as shown in FIG. 7e or, in
the extreme case, providing local service only as shown in FIG.
7d). In this way, local and express service can remain available
for every customer, with local service following the schedule
during non-peak times as during peak usage times, while system 20
is provided with the ability to respond to peak rush hour usage
without necessarily altering the schedule.
[0151] FIGS. 8a through 8c illustrate an optimum sequence by way of
which trains may arrive at and depart an express station according
to this embodiment of the invention. As evident from the foregoing
description, train wait times constitute an important factor in the
overall travel time of each passenger along subway line SLINE.
According to this embodiment of the invention, in which a first
train of a group arriving at an express station at the same time is
transforming from local service to express service (such a train
referred to herein as an "LE" train) while the last train in the
same group of trains arriving at that express station is
transforming from express service to local service (such a train
referred to herein as an EL train), the later-arriving trains in
the group can be forced to wait for the first train (the LE train)
to leave the platform. Any time that elapses while the second and
remaining trains are stopped at an express station short of the
platform and waiting for the first train to leave is not only
wasted travel time that lengthens the time of the overall trip, but
is also annoyingly noticeable to the passengers on the stopped
train. It is therefore beneficial to minimize such waiting time at
the express stations.
[0152] FIGS. 8a through 8c illustrate the operation of a
three-train group, similar to that described above relative to FIG.
7b, in stopping at platform 50 of an express station. At the point
in time shown in FIG. 8a, train T60 is stopped at platform 50, with
passengers boarding and de-boarding train T60 at that time. Train
T60 is an LE train, in that it had provided local service over the
express interval leading up to platform 50, but will provide
express service over the next interval. Train T62 is the next train
to arrive at platform 50, and has been providing express service
over the preceding express interval. At the point in time shown in
FIG. 8a, train T62 is still moving toward platform 50, but has not
yet arrived. Similarly, train T64 is the last train in this
three-train group, and trails train T62 by some distance; train T64
is an EL train at this point in time, as it is currently providing
express service over the express interval preceding platform 50 but
will provide local service over the interval following platform
50.
[0153] FIG. 8b illustrates a point in time later than that shown in
FIG. 8a, at which train T60 has already left platform 50 and is
proceeding along the next express interval, and will be providing
express service. Train T62 is now at platform 50, with passengers
boarding and de-boarding train T62 during this time. Train T64 is
still some distance away from platform 50. Again, both of trains
T60, T64 are moving during the time that train T62 is stopped at
platform 50. FIG. 8c depicts a later point in time than that of
FIG. 8b, at which time train T62 has now also left platform 50 and
at which train T64 is stopped at platform 50. Passengers who wish
to stop at a local station along the next express interval from
platform 50 will be boarding train T64 at this time, and passengers
on train T64 who are terminating their trip at this station will be
de-boarding.
[0154] It is contemplated that system 20 can schedule and manage
the velocities of trains T60, T62, T64 to optimize the efficiency
of the stop of each train at platform 50. As such, the particular
distances between trains T60, T62, T64 in this example shown in
FIGS. 8a through 8c can vary. However, it is contemplated that
system 20 can optimize these spacing distances in a manner that
minimizes the time that each train T60, T62, T64 is stopped at or
before platform 50, and that also minimizes the time between the
departure of one train and the arrival of the next. In other words,
the scheduling and operation of trains T60, T62, T64 can be managed
by system 20 to minimize the wait times for those passengers
transferring from one of trains T60, T62 to train T64, while also
eliminating any time that a later train is stopped short of
platform 50, waiting for a train currently at platform 50 to
leave.
[0155] If the later-arriving trains (trains T62, T64 in the example
of FIGS. 8a through 8c) need not slow appreciably in order to
minimize the wait times in the manner described above, those
later-arriving trains can then maintain full express service.
However, in some cases, the arrangement of subway line SLINE will
require full express trains to slow significantly in order to not
be forced to wait for platform 50 to open at the next express
station. According to another embodiment of the invention, as will
now be described in connection with FIGS. 9a through 9c, the
available additional time can be used to further improve service by
including "semi-express" stations into the schedule.
[0156] FIG. 9a illustrates an express interval along subway line
SLINE between express stations E0 and E1. Local stations L1, L2,
L3, L4 are located along this interval. At the point in time
illustrated in FIG. 9a, train T63 has arrived at express station
E1, having provided local service over the interval between express
stations E0 and E1. Train T65 is next to arrive at express station
E1, and has been providing express service along that same
interval. According to the transformation embodiments of this
invention, train T63 will provide express service over the interval
following express terminal E1 (i.e., train T63 is an LE train), and
train T65 will provide local service over that next interval (i.e.,
train T65 is an EL train). Rather than unduly slow the travel
velocity of train T65 to eliminate its wait time at express station
E1, train T65 makes one local stop along the interval between
express stations E0 and E1, specifically at local station L3 in the
example of FIG. 9a. By making this additional stop, the arrival
time of train T65 can be managed so that it arrives at express
station E1 "just in time", as train T63 pulls out of the station.
In addition, local station L3 receives the benefit of
"semi-express" service, in that passengers may board and de-board
train T65 at that station, and travel to express station E1 without
making a stop at intervening local station L4.
[0157] FIG. 9b illustrates a variation of this semi-express
embodiment of the invention, for the case of a three-train group of
trains T66, T68, T70 proceeding along the same interval. At the
point in time shown in FIG. 9a, train T66 is stopped at express
station E1, after having provided local service along the interval
between express stations E0, E1 (and thus having stopped at each of
local stations L1, L2, L3, L4). Train T66 is an LE train, and such
will provide express service along the interval after express
station E1. Train T68 will be the next train to arrive at express
station E1 after train T66 leaves; this train T68 has provided
express service over the interval between express stations E0 and
E1, and as such will be catching up to LE train T66 (optimally) as
train T66 leaves express station E1. As such, train T68 has made no
stops along this interval since it left express station E0. In this
example, however, third train T70 follows train T68, and is
providing express service (and, indeed, will be an EL train at
express station E1, beginning local service over the next
interval). Because two trains T66, T68 are ahead of tail train T70
in this example, train T70 makes one local stop along the interval
between express stations E0 and E1, specifically at local station
L3 in this example. By making this additional stop, the arrival
time of train T70 can be managed so that it arrives at express
station E1 "just in time", as train T68 pulls out of the station.
In addition, local station L3 receives the benefit of
"semi-express" service, in that passengers may board and de-board
train T70 at that station, and travel to express station E1 without
making a stop at local station L4. FIG. 9b also illustrates an
alternative for second train T68, in which it makes a semi-express
stop at local station L4 to eliminate its wait time at express
station E1 (waiting for train T66 to leave). Local station L4 in
this case is also provided with semi-express service, at little or
no cost to the overall travel time of train T68 along subway line
SLINE.
[0158] FIG. 9c illustrates a similar example of semi-express
operation, in connection with a four-train group. In this example,
train T72 is the LE train, and has arrived at express station E1
after having provided local service along the interval. Train T74
is a train providing express service over the interval immediately
following train T72, and will arrive at express station E1 just
after train T72 has left. To more efficiently manage the arrival of
train T74 at express station E1, train T74 has made one
semi-express stop along the interval, at local station L4 in this
example. Train T76 will be the next to arrive at express station E1
after train T74 and, in this case, will make one semi-express stop
at station L3 (which is an earlier stop, west-to-east, along subway
line SLINE than is station L4 at which train T74 makes a
semi-express stop). Train T78 is the fourth train in this group,
and will be the EL train at express station E1. Train T78 also
makes a semi-express stop, at station L2 (which is earlier stop,
west-to-east, than semi-express stations L3 and L4). Optionally,
train T78 can make another semi-express stop along this interval,
for example at local station L3, to further delay its arrival at
express station E1 until after train T76 has left the station. FIG.
9c thus illustrates that no correlation necessarily exists between
the position of a train within a group and the number of
semi-express stops made along an express interval. Rather, the
number, timing, and locations of semi-express stations over an
interval depends on the particular situation.
[0159] According to this embodiment of the invention, the addition
of semi-express stops within an express interval provides
additional flexibility in the scheduling of the arrival of express
service trains at an express station. This additional flexibility
enables productive use of any delay time involved in minimizing the
wait time at an express station, by providing semi-express service
at one or more stops along the express interval, thus providing
both an additional train to passengers boarding at those stations,
and in many cases providing a faster trip for those passengers to
the next express station. It is contemplated that system 20 can
incorporate such semi-express stops into the optimization that it
carries out in connection with subway line SLINE, incorporating
such factors as passenger demand and the like. In addition, the
particular arrangement of semi-express stops can be altered from
that shown in FIGS. 9a through 9c. These and other constraints and
alternatives may be included in the schedule and management
optimization carried out by system 20.
[0160] Local to Express Train "Transformation" with "Passenger
Relay"
[0161] In the embodiments of the invention described above, subway
line SLINE and its express stations are operated in a
first-in-first-out manner. In this approach, the first train of a
group to arrive at an express station is the first to leave, making
it impossible for a passenger to transfer from a later-arriving
train in a group to an earlier-arriving train in that group. While
benefits of this invention are still attained even with that
complication, subway line SLINE and its trains can be operated in a
manner that enables forward transfer of passengers in an efficient
manner, according to other embodiments of this invention. As a
result, not only can passengers more efficiently travel from any
local station to any other local station, but as will become
evident below, according to this embodiment of the invention,
ambitious passengers are provided with the ability to travel nearly
their entire trip at the faster express velocity, by making
strategic forward-moving transfers at express stations.
[0162] According to these embodiments of the invention, the virtual
passing provided by local to express train transformation, as
described above in connection with FIGS. 6, 7a through 7c, 8a
through 8c, and 9a through 9c, enables passengers to forward
transfer from train to train at each express station. More
specifically, these embodiments of the invention enable passengers
on an express train to transfer from an EL train (i.e., an express
train that is transforming to a local train) to an LE train (i.e.,
a local train that is transforming to an express train). In other
words, passengers may remain on an express train throughout the
duration of the trip, to the extent that the passenger is traveling
the full length of intervals between express stations. As will
become evident from this description of these embodiments of the
invention, according to this "passenger relay" approach, passengers
are provided with the option of actually traveling faster than the
fastest train traveling along subway line SLINE. It is contemplated
that this mode of travel will have most appeal to regular commuters
who are familiar with the actions required on their part to make
these forward transfers, and perhaps to younger commuters who are
able to rapidly change trains in a forward direction.
[0163] FIGS. 10a through 10d illustrate the operation of trains
T80, T82 in a two-train group, in making stops at platform 50 at
express station E.sub.x according to an embodiment of the invention
in which passengers may make a forward train-to-train transfer.
According to this embodiment of the invention, platform 50 is made
accessible to passengers in the rear-most train of a group of
trains before it is made accessible to the front-most train in that
group. At the point in time shown in FIG. 10a, this forward
transfer is facilitated by front-most train T80 (the LE train in
this example) stopping with its rear portion at platform 50, and by
rear-most train T82 (the EL train in this example) stopping with
its front portion at platform 50. In this state, access from
platform 50 is provided to both of trains T80 and T82. More
importantly, for purposes of the passenger relay operation,
platform 50 is made available to some passengers in rear-most train
T80.
[0164] For best efficiency, it is useful to control (or at least
encourage) access to platform 50 during this initial stop so that
only forward transfer passengers de-board rear-most train T82, and
so that no passengers board or de-board front-most train T80. FIG.
10b shows the desired relay passenger flow from the front half of
train T82 to platform 50, with those de-boarding passengers then
moving toward the downtrack side of platform 50. The doors to train
T80 may remain closed during this time, to prevent passenger
ingress and egress. By limiting (or encouraging limited) passenger
access to platform 50 with trains T80, T82 sharing platform 50, the
stop time required for this procedure can be minimized.
[0165] Following the de-boarding by forward transfer passengers in
FIG. 10b, both trains T80, T82 close their doors, and then back up
a portion of their lengths so that train T80 is then stopped along
the length of platform 50. Passengers now board and de-board train
T80 from and to platform 50. In addition, those forward transfer
passengers who de-boarded train T82 during the transfer stop of
FIGS. 10a and 10b now board the front part of train T80, as shown
in FIG. 10c. In this way, those same passengers are in the correct
position to de-board train T80 to make a subsequent forward
transfer to the next train ahead of train T80, at the next express
station E.sub.x+1, in the same manner as just now accomplished at
express station E. Passengers in the front portion of train T80 can
now de-board to platform 50 as desired. Upon completion of the
boarding and de-boarding of train T80 in FIG. 10c, train T80 then
leaves express station E.sub.x, providing express service (or
semi-express service, if the approach described above relative to
FIGS. 9a through 9c is implemented) over the next express interval.
Train T82 then pulls forward to platform 50 (FIG. 10d), to allow
its local passengers to board and de-board in the conventional
manner.
[0166] As shown in FIGS. 10a through 10d according to this
embodiment of the invention, passengers on an arriving express
train that is about to transform into a local train (e.g., train
T82) are permitted to transfer to a train that is about to
transform from local service to express service (e.g., train T80).
These forward transferring passengers will thus arrive at their
desired destination earlier than will train T82 upon which they
were riding. By continuing this forward transfer process at each
express station, those passengers can ride along subway line SLINE
at express travel velocities over most if not all of the entire
length of their trip (short of any local interval necessary if the
trip originated or terminates at a local-only stations). Meanwhile,
those passengers who do not wish to take advantage of the passenger
relay option still obtain the benefit of express service over a
portion of their trip, namely over those intervals during which
their train is traveling at express travel velocity. However,
according to this embodiment of the invention, the stop time at
express station E.sub.x could increase unless passenger access to
platform 50 is controlled or encouraged to take place in the manner
described above.
[0167] FIGS. 10e through 10g illustrate another implementation of
this embodiment of the invention, in which the passenger relay is
limited to a few forward cars of the arriving EL train, but in
which passenger movement among the cars of a given train is
permitted (and is physically possible, within the constraints of
passenger loading within each train). With the constraint of
intra-train passenger movement relaxed, the time required for
passenger transfer and loading/unloading at express stations can be
reduced. FIG. 10e illustrates a first stage of the process, in
which LE train T80 and EL train T82 are first stopped at platform
50 of express station E. In this implementation, each of trains
T80, T82 have ten cars, and the initial stop of LE train T80 at
platform 50 places only a selected number of the rear-most cars
(e.g., eight cars) at platform 50; the remaining forward-most cars
(e.g., two cars) are past platform 50 in this initial stop.
Later-arriving EL train T82 stops at platform 50 behind train T80,
and its forward-most cars (e.g., two cars) are aligned at platform
50. This initial stop allows passengers to begin making the relay
between EL train T82 and LE train T80, but only from these
forward-most cars. These passengers de-board EL train T82, and walk
the length of platform 50 to an area corresponding to the
forward-most cars of LE train T80, but they do not board train T80
at this time.
[0168] Trains T80, T82 both back up after the operation of FIG.
10e, to the position shown in FIG. 10f in which all cars of LE
train T80, including the forward-most cars, are aligned with
platform 50. Boarding and de-boarding of train T80 is now
permitted, relative to all cars. During this portion of the stop,
the relay passengers who de-boarded EL train T82 (FIG. 10e) can now
board the forward-most cars of LE train T80, along with the other
boarding and de-boarding passengers. LE train T80 can then leave
station E.sub.x upon completion of this process, and begin express
service over the next express interval; after train T80 leaves, EL
train T82 pulls forward to platform 50 for its boarding and
de-boarding operations (including the boarding of LEL transferring
passengers from train T80), as shown in FIG. 10f. To assist in the
flexibility of this passenger relay operation, passengers on train
T80 can now move from car-to-car, as suggested by the arrow in FIG.
10g. In this way, LEE and LEL passengers who boarded train T80
during the previous express interval can move into the forward-most
cars and begin their passenger relay journey; meanwhile, those
passengers who will be transferring to local service at the next
express station can move into the rear-most cars to reduce
overcrowding. It is contemplated that on-train displays, or perhaps
also the ticketing (e.g., e-ticketing) process can instruct
individual passengers regarding their optimal movement from
car-to-car within a train, as well as from train-to-train as
discussed above.
[0169] Substantial time can be saved in the stops at express
stations according to this implementation of FIGS. 10e through 10g.
The time savings stems primarily from the reduced length over which
the trains must back up to complete the transfer. And, as discussed
in this specification, because express station stop times are
repeated multiple times over the length of subway line SLINE, and
are directly included as an adder to each passenger's travel time,
reduction in the express station stop time is of particular
importance in improving passenger and train travel time along
subway line SLINE, and thus passenger throughput.
[0170] It is of course contemplated that variations on the manner
in which the passenger relay process is enabled at each express
station, including the number of rear-most cars to be aligned at
each express station platform for a given passenger demand and
train density, can vary from time-to-time during the day. Indeed,
it is contemplated that the alignment of trains at express station
platforms to permit passenger relay operations can be optimized by
system 20 in its generation of the schedule and operational
parameters within the overall process of FIG. 3b.
[0171] The passenger relay concept can be extended to train groups
of more than two trains. FIGS. 11a through 11c illustrate the stop
operation at express station E.sub.x for the example of a
three-train group of trains T84, T86, T88. Front-most train T84 is
the LE train in this group, and rear-most train T88 is the EL train
in this group; middle train T86 provides express service over both
intervals, before and after express station E. The first stage of
the stop at express station E.sub.x is illustrated in FIG. 11a, in
which train T84 pulls past platform 50, and trains T86, T88 both
align at platform 50 so that access is provided to portions of both
trains simultaneously. This stop position in FIG. 11a allows
forward transfer passengers to de-board EL train T88, and enables
passengers to both board and de-board train T86 from platform 50.
In FIG. 11b, a next stage in this stop has trains T84, T86 both
aligned with platform 50. This allows passengers to board and
de-board the rear-most portion of train T84. In addition, during
this time, the forward transfer passengers from EL train T88 are
now able to board either the rear-most portion of train T84 or the
front-most portion of train T86. Those forward transfer passengers
who will be making another forward transfer at the next stop will
wish to board the front-most portion of train T86, as this train
will be an EL train at the next express station E.sub.x+1 and thus
these passengers will wish to de-board train T86 at the first stage
at that station (as shown in FIG. 11a). The stop at express station
E.sub.x for this three-train group is shown in FIG. 11c, in which
EL train T88 stops along the length of platform 50 after trains
T84, T86 have left the station; local passengers can then board and
de-board train T88.
[0172] The operation of a stop at express station E.sub.x for a
two-train group of trains T90, T92 is illustrated in FIGS. 12a
through 12c, for one example of this embodiment of the invention.
In this example, each of trains T90, T92 has a length that is about
one-half the length of platform 50, and in this case each train
consists of four train cars. In the first stage of this stop shown
in FIG. 12a, front-most train T90 (the LE train) occupies the front
half of platform 50, and rear-most train T92 (the EL train)
occupies the rear half of platform 50. In this first stage,
passengers terminating their trip at express station E.sub.x can
de-board train T90; express passengers (EEE passengers) who wish to
board an express train at station E.sub.x can board train T90 at
this time, as shown in FIG. 12a. Those passengers wishing to
transfer from express service (train T90) to local service over the
next interval (on train T92) also deboard train T90 during this
first stage of the stop. Also at this point in time, those
passengers wishing to make the relay from EL train T92 to LE train
T90 (i.e., who wish to continue from one express train to the next)
de-board train T92 to platform 50, but remain at the rear portion
of platform 50. In a next stage of the process, shown in FIG. 12b,
trains T90 and T92 move backward, aligning train T90 with the rear
portion of platform 50. The forward transfer passengers from EL
train T92 can now board train T90. The final stage of this stop is
shown in FIG. 12c, with EL train T92 stopped along the front
portion of platform 50 to receive local passengers; by this time,
train T90 has already left express station E.
[0173] In this approach illustrated in FIGS. 12a through 12c,
passenger relay is accomplished in a manner that minimizes the
necessary movement of the relaying passengers, at a cost of
requiring the trains to move back and forth along the station
platform. According to another approach, as will now be described
in connection with FIGS. 12d and 12e, the stop time of the trains
at the express stations is minimized, at a cost of requiring the
relaying passengers to move along the station platform.
[0174] FIG. 12d shows express station E.sub.x at a first stage of
the stop of LE train T90 and EL train T92, both of which have a
length approximately of one-half the length of platform 50. In this
first stage, train T90 occupies the front half of platform 50 and
train T92 occupies the rear half of platform 50. At this time, as
shown in FIG. 12d, passengers terminating their trip at express
station E.sub.x can de-board train T90, and EEE passengers can
board train T90. Also at this point in time, those passengers
making the relay from EL train T92 to LE train T90 (i.e., who wish
to continue from one express train to the next) de-board train T92
to platform 50 and move along platform 50 directly over to train
T90, which they board. In the second stage of the stop, as shown in
FIG. 12e, train T92 stops at the front portion of platform 50 after
train T92 has left express station E.sub.x, to receive local
passengers, including those who de-boarded train T90 during the
first stage of the stop. As a result of this approach, LE train T90
only has to make a single stop along platform 50, because the relay
passengers move from train T92 to train T90, rather than train T90
moving to the relay passengers as in the case of FIGS. 12a through
12c.
[0175] FIG. 12f illustrates another alternative to these two
approaches, in which both transferring and relaying passengers move
from train to train, allowing both the LE train and the EL train to
make a single stop at express station E. FIG. 12f illustrates the
passenger movement between LE train T90 and EL train T92; the
movements of passengers boarding and de-boarding either train from
or to express station E.sub.x are shown by horizontal arrows in
FIG. 12f. In this example, relay passengers exit EL train T92, walk
along platform 50, and board LE train T90; conversely,
express-to-local transferring passengers exit LE train T90, walk
along platform 50 in the opposite direction, and board EL train
T92. It is contemplated that markings or temporary barriers or some
other physical assistance to the relay and transfer passengers at
platform 50 can facilitate the passenger movements involved.
Following the passenger movement in this single stop at platform
50, both trains T90, T92 can depart express station E. In this
regard, it may be useful for closed-circuit television or some
other real-time monitoring of express station E.sub.x can be used
to allow sufficient time for all movement between trains and other
boarding activity, such that the departure of trains T90, T92 can
be done as soon as possible while allowing passengers to complete
their transfers.
[0176] As discussed above, the number of trains per group can be
increased during peak times, in order to improve passenger
throughput and passenger travel times, without necessarily changing
the schedule of local service, considering that local trains are
the pacemakers along subway line SLINE. It is further contemplated
that express service can be provided along subway line SLINE even
if demand in off-peak times is very low, and it is further provided
that transfers and passenger relay operation can be enabled even
with that low passenger demand, as will now be described in
connection with FIGS. 12g and 12h.
[0177] In the alternative shown in FIG. 12g, each of LE train T94
and EL train T96 at express station E.sub.x is a half-length train,
relative to the lengths shown in FIGS. 12a through 12f. Similarly
as in the case of FIG. 12f, FIG. 12g illustrates the passenger
movement between train T94 and T96 in both directions. As such,
relay passengers exit EL train T96, walk along platform 50, and
board LE train T94 simultaneously with express-to-local
transferring passengers exiting LE train T94, walking along
platform 50 in the opposite direction, and boarding EL train T96.
Following the passenger movement in this single stop at platform 50
(and any boarding and de-boarding of originating or terminating
passengers at express station E.sub.x, not shown in FIG. 12g), both
trains T94, T96 depart express station E.sub.x in succession.
Similarly, FIG. 12h illustrates the same operation in connection
with LE train T98 and EL train T99, each of which are
minimum-length trains constituting a single car in each. Also in
this example, each of trains T98, T99 make a single stop, and all
relay and express-to-local transfers are made during that stop,
along with boarding and de-boarding from and to express station E.
These shorter-length trains as shown in FIGS. 12g and 12h enable
the subway operator to continue to provide express service without
disrupting the local train schedule, even at off-peak times in
which ridership is otherwise very low.
[0178] In each of these examples shown in FIGS. 12a through 12h,
passengers from the rear-most train of a group, that rear-most
train transforming from express to local service at the express
station, can transfer forward to a train that will be providing
express service over the next interval. This passenger option
allows these relay passengers to travel faster than any given train
along subway line SLINE, while also allowing passengers not wishing
to make the forward transfer with shorter travel times as well.
[0179] It is contemplated that system 20 will be able to comprehend
the forward transfer option and processes, and to notify passengers
of the option and the boarding (i.e., car assignment) and transfer
procedures necessary to optimally use passenger relay for each
passenger's specific journey. Graphics or video displays on the
trains or at the stations can be driven by system 20 to advise
passengers of these options and procedures, or system 20 can advise
the passengers via the ticketing process (especially if
point-to-point ticketing is used).
[0180] FIGS. 13a through 13d show one example of the manner in
which system 20 can communicate boarding and transfer instructions
to passengers at a station of origin, and perhaps also at an
express station at which a relay or express-to-local transfer is
permitted. As shown in the plan view of FIG. 13a, platform 50 is
conceptually divided into two equal length platform portions 50b,
50p, each color-coded blue and pink, respectively, with blue
platform portion 50b downtrack from pink platform portion 50p. At
the point in time shown in FIG. 13a, two trains T102, T104 are
stopped at platform 50, with train T102 aligned with blue platform
portion 50b and train T104 aligned with pink platform portion 50p.
FIG. 13b is an elevation view of the middle portion of platform 50
at which trains T102 and T104 abut one another at this stop; as
shown in FIG. 13b, car C102e is the last car of train T102 and car
C104a is the first car of train T104. Graphics displays 106b, 106p
are mounted above platform 50, overhanging blue and pink platform
portions 50b, 50p respectively, to provide well-visible
instructions to passengers boarding cars C102e, C104a. FIGS. 13c
and 13d illustrate an example of the information displayed on
graphics displays 106b, 106p, respectively, at the time that trains
T102, T104 are stopped at this station. Each of graphics displays
106b, 106p display the platform portion color (e.g., blue and
pink), the train number of the trains current stopped at those
platform portions 50b, 50p (or approaching the station, if not yet
arrived), and a list of those stations at which a passenger
boarding a train stopped or soon to stop at platform portions 50b,
50p will be able to stop without a transfer. In embodiments of this
invention, system 20 will drive graphics displays 106b, 106p with
the appropriate information for the current or upcoming stop at
that particular station, to assist passengers in boarding the
optimum train car or transferring between trains to accomplish
their trip in the most efficient manner.
[0181] In addition, system 20 may alter the particular processes
and stages implemented at the express stations from those described
above in connection with FIGS. 10a through 10d, 11a through 11c,
and 12a through 12c, as appropriate to further optimize the
operation of the subway system for passenger travel time, passenger
throughput, infrastructure and rolling stock optimization, and the
like. Those updates can, of course, also be communicated to
passengers by way of at-station graphics displays 106b, 106p (FIGS.
13a through 13d), by way of on-train graphics displays, or in the
ticketing process as described above.
[0182] Regardless of whether the passengers make the forward
transfers, because of the ability to travel at least part of the
trip on subway line SLINE at express velocity V.sub.exp, it is
contemplated that the passenger travel time on subway line SLINE
will be reduced for many, if not all, passengers according to this
embodiment of the invention. It is also contemplated that the
ability of system 20 according to this embodiment of the invention,
in displaying schedules and train assignments, and perhaps
individual tickets for specific station-to-station trips, can
reduce confusion on the part of the subway passengers in navigating
subway line SLINE, especially for commuting trips in which the
passengers can become used to the best way to make their desired
trips. Overall efficiency in the travel of many passengers, and in
the utilization of the subway system including reduction in
overcrowding by improving the passenger throughput, is therefore
expected to be readily attained through use of this embodiment of
the invention.
[0183] Schedule and Operational Optimization
[0184] General Methodology
[0185] As described above relative to FIGS. 3a and 3b, process 38
is executed by system 20 to derive a schedule for the trains along
subway line SLINE so that express and local trains traveling in the
same direction meet only at express stations. It is contemplated,
according to this invention, that process 38 will be carried out by
system 20 according to an optimization algorithm, in which a cost
function is established and minimized by iteratively changing
parameters that define the schedule being derived. The particular
cost function being minimized in deriving the schedule may seek to
optimize any one or more of a number of parameters, such as
passenger throughput, passenger travel times over a population of
passengers, infrastructure demands, and the like. Schedule
parameters that may be changed in each iteration include such
factors as train departure times, train interval velocities, number
of trains in a group, boarding and de-boarding times and sequences
at express and local stops, and the like.
[0186] A close relationship exists between a subway line system and
the passenger volume on a given subway line, in that each depends
on the other. The definition of a schedule for the subway line
system, and particularly the optimization of that schedule,
requires interacting the subway line system itself with the
passenger volume on that line. Efficiency of the system in light of
passenger demand is best served by defining applicable system
parameters, and the characteristics of the passenger volume.
According to embodiments of this invention, these parameters and
characteristics can be analyzed in a manner corresponding to the
following Table 2:
TABLE-US-00002 TABLE 2 Train density Theor. Express Train (per
pass. Pass. Train Trains trains length express Local Pass. travel
travel group Passing per per (wrt station train thruput time time
pass. Technique Manner FIGS. group group platform) interval) equiv.
per train saving saving thruput Physical Side- 1b-1d; 2 1 1 3 4 1.3
50% ~45% 2.66 passing track 7e-7g 3 2 1 4 6 1.5 50% ~43% 4.5 4 3 1
5 8 1.6 50% ~40% 6.4 Side- 4a-5o 2 1 1 3 4 1.3 50% ~45% 2.66
by-side 3 2 1 4 6 1.5 50% ~43% 4.5 station 4 3 1 5 8 1.6 50% ~40%
6.4 Local trains only 7d 1 0 1 2 2 1 0% 0% N/A Virtual Local to 7a
& 7e 2 1 1 3 4 1.3 25% ~20% 2.66 passing express 7b & 7f 3
2 1 4 6 1.5 33% ~30% 4.5 xform 7c & 7g 4 3 1 5 8 1.6 41% ~35%
6.4 Local to 10a-10g 2 1 1 3 4 1.3 50% ~45% 2.6 express 11a-11c 3 2
1 4 6 1.5 50% ~45% 4.5 xform 12g-12h 2 1 0.5 3 4 0.66 50% ~45% 1.33
with pass. 2 1 0.2 3 4 0.26 50% ~46% 0.53 relay 2 1 0.1 3 4 0.13
50% ~47% 0.26
Table 2 summarizes performance characteristics for examples of
embodiments of the invention described above. More specifically,
the "Passing Technique" column groups the approaches of those
methods into those in which express trains physically pass local
trains at an express station, and those in which the passing is
"virtual" in the sense that specific physical trains transform
their service from local-to-express, and express-to-local, at
express stations. The detailed description corresponding to each
implementation is indicated by way of reference to its
corresponding Figure or Figures. Various performance parameters for
each individual implementation are shown in a normalized form,
relative to conventional "local-only" service in which all trains
on the subway line provide local service. In Table 2, the column
"Trains per group" designates the number of trains in each group
that meet at an express station; the column "Express trains per
group" indicates the number of trains providing express service in
each group, and each of these implementations assume a single local
train in each group. The "Train length" column indicates the length
of each train relative to a standard platform length. Based on
those assumptions, the "train density" is indicated in the next
column, referring to the total number of local and express trains
physically present over each express interval.
[0187] Based on those assumptions, the remaining columns beginning
with "Local train equivalent" are essentially calculated values.
The column "Local train equivalent" is derived by considering the
number of trains within an express interval are express trains
(assumed to be traveling at twice the average travel velocity of a
local train), in combination with the train density over an
interval. In short, "Local train equivalent" is calculated as:
(Local train equivalent)=2+2*(Express trains per group)
This is because two local trains are present within each express
interval at any given time. For example, a two-train group results
in two local trains and one express train within an express
interval at any given time; because the express train is traveling
at twice the travel velocity as the local trains, an express train
can transport twice as many passengers than can a local train over
a given time duration. Therefore, the equivalent passenger capacity
in terms of local-only trains is four. The column "Passenger
throughput per train" reflects this same parameter in terms of the
Local train equivalent divided by the Train density within the
express interval.
[0188] The "Theoretical passenger travel time savings" column
refers to the time that a passenger would save by virtue of the
ability to travel at express travel velocities, relative to
traveling via local-only service, and assuming no additional time
required for physical or virtual passing at the express stations.
For example, in two-train groups operated according to the physical
passing technique, a passenger would be traveling at express travel
velocity for the duration of his or her journey, in which case the
travel time savings would be 50% (express travel velocity being
twice local travel velocity). For two-train groups involving
virtual passing (and no passenger relay), a passenger would be
traveling at express travel velocity over alternating express
intervals (i.e., about half the time), during which time his or her
travel velocity would be twice that of the local travel velocity
over the other intervals; this amounts to a 25% theoretical
passenger travel time saving. And for two-train groups involving
virtual passing with passenger relay, a passenger becomes able to
travel at express velocities over the full duration of the journey,
thus achieving the theoretical travel time saving of 50%.
[0189] It is contemplated that those skilled in the art can readily
comprehend these performance criteria as summarized, by way of
example, in Table 2. Among other conclusions, it can be seen from
Table 2 that the physical passing techniques can theoretically
attain a passenger travel time saving of 50%, as all express trains
continue to provide express service, at express travel velocity,
over the entire length of the journey. In addition, Table 2
summarizes that the passenger relay method applied to the virtual
passing techniques can also attain this 50% theoretical passenger
travel time saving. According to Table 1, because of the ratio of
express and local train operation intervals, the theoretical
passenger travel time saving for the two, three, and four train
group virtual passing (without passenger relay) case are 25%
[(3/6)*0.5*100], 33% [(4/6)*0.5*100], and 41% [(5/6)*0.5*100],
respectively. And as described above, the virtual passing
techniques can be applied to existing subway lines, without
requiring construction or excavation or other changes to
infrastructure as necessary in the physical passing context.
[0190] Extra-Train Delay Time
[0191] As mentioned above, however, the theoretical passenger
travel time saving assumes no time is involved in the passing
operations at express stations. This is, of course, unrealistic for
both the physical and virtual techniques, considering that time
must be allotted for passenger transfer (local-to-express, and
express-to-local). Table 2 includes the column "Passenger travel
time saving", which includes the effect of the delay time for
passenger transfer at express stations, as will now be
described.
[0192] As a concept, an understanding of the delay time required
for passenger transfer is simple. However, it has been observed, in
connection with this invention, that it is cumbersome to actually
estimate this extra-train delay time (EDT) to any precision,
because EDT depends on the passing method, on the number of trains
in a group, and on other factors including train length relative to
the platform length. More specifically, one must estimate the stop
time for a local train at a local station (LLST), and the stop time
for a local train at an express station (LEST); the difference
between the local-train express-station stop time (LEST) and the
average local train stop time (ALST) determined as the average
local-train local-station stop time (LLST) over all of the local
stations of subway line SLINE, which tends to be a stable quantity.
The calculation of EDT differs between the physical passing and
virtual passing methods. Under the physical passing case, in which
local trains remain local and express trains remain express, the
quantity LEST can be defined as the time elapsed between the
arrival of the local train at the express station, and the
departure time of that local train from the express station,
assuming the number of trains per group exceeds one (i.e., at least
one express train passes the local train at the express station).
Under the virtual passing case, the quantity LEST is defined as the
time elapsed from the LE train (i.e., the first train in the group)
arriving at the express station and the departure of the EL train
(i.e., the last train in the group). The quantity EDT for both
cases is then defined as EDT=LEST-ALST.
[0193] Consistent with these definitions and based on the
description of these passing methods in this specification, one can
deduce that the quantity EDT will vary from one passing method to
another, and also will vary with the length of the trains involved.
Those variations in EDT will be reflected in the proximity of the
"Passenger travel time saving" value to the "Theoretical passenger
travel time saving" shown in Table 2 for the various operational
methods. That proximity will result from the calculations of total
passenger travel time over subway line SLINE, based on the
schedules derived by system 20 in connection with scheduling
process 38, as will now be described.
[0194] As described above, scheduling process 38 is executed by
system 20 to derive and, if desired, modify the scheduling of
trains along subway line SLINE in response to passenger data 33,
train data 35, and station data 37, and according to the definition
of certain stations and trains as express and local stations and
trains, respectively. It is contemplated that scheduling process 38
will serve to optimize the derived and modified schedule according
to a criteria selected by the subway system operator. It is further
contemplated, according to this invention, that a particularly
beneficial approach to scheduling process 38 is to optimize the
schedule in order to minimize total passenger travel time over
subway line SLINE. The passenger travel time being minimized may be
that for a trip over the entire length of subway line SLINE, or
alternatively may be a cumulative or average passenger travel time
value taken over a typical population of passengers, or some other
population. Fundamentally, this optimization of passenger travel
time depends on a wide range of factors, including the particular
passing method used (i.e., physical or virtual passing); the
lengths of trains and platforms; the time of day; the type of day
such as workday, weekend, or holiday; passenger demand by station;
and the like. These additional factors are, in general, dependent
on the characteristics of the subway system and the city being
served, and as such can be considered as installation-dependent.
For purposes of this description, however, it is believed useful to
describe some of the factors involved in the optimization of the
schedule from the standpoint of minimizing passenger travel time,
as it is contemplated that this optimization will be an important
goal of implementations of embodiments of this invention in
practice.
[0195] For purposes of simplicity and clarity of this description,
the above discussion summarized in the column "Theoretical
passenger travel time savings" of Table 2 has been based on two
assumptions: first, that the length of each train and the length of
the platform at each station are each zero; and second, that all
trains of a group arrive at and depart from each express station at
the exact same time. In effect, the extra-train delay time (EDT)
was assumed to be zero. Of course, in practice, those two
assumptions do not hold.
[0196] In order for scheduling process 38 to actually minimize
passenger travel time, according to embodiments of this invention,
additional parameters are considered. For reference purposes, it is
useful to consider the baseline operational times of a local-only
train in traveling an express interval, including the time involved
in making a stop at an express station. This local-only travel time
(LETT) of the i.sup.th express station can be more accurately
described as the difference between the time at which the
local-only train arrives at express station E.sub.i (e.g., the time
at which the head car of this arriving eastbound train reaches the
easternmost endpoint of platform 50e of FIG. 4a), time at which
that train departed the previous express station E.sub.i-1 (e.g.,
the time at which the head car of this departing eastbound train
leaves the easternmost endpoint of platform 50e). Also under
consideration for that interval is the time required for the
local-only train to make its stop at express station E.sub.c. For
purposes of this description, one can use the average local train
express station interval stop time (ALST), which tends to be a
stable quantity. The local-only train express-station-interval
operation time (LEOT) can then be defined as the sum:
LEOT.sub.1=LETT.sub.1+ALST
This baseline local-only train operation time of the i.sup.th
express station interval LEOT.sub.i is also a factor in the
operation of a group train according to embodiments of this
invention described above, except that the group train
express-station-interval operation time (GEOT.sub.i) also requires
consideration of the extra-train delay time (EDT) amounting to the
additional delay time of a group train at an express station:
GEOT.sub.i=LEOT.sub.i+EDT
[0197] As mentioned above, EDT varies according to the passing
method used, and also varies with the number of express trains
within the group, such that EDT=EDT(m, j), where m refers to the
passing method and j indicates the number of trains within a group.
In any case, extra-train delay time EDT depends on such factors as
the not-insignificant time required for the head of the train to
move the length of the platform (the instantaneous velocity of the
train being relatively slow, for safety reasons) and also the time
required for the tail of a preceding train to clear the length of
the platform as that train departs (the instantaneous velocity of
that train also being relatively slow).
[0198] As discussed above, in the general sense, the local-only
train operation time LEOT will spatially vary, being different for
different express intervals:
LEOT.sub.1.noteq.LEOT.sub.2.noteq.LEOT.sub.3.noteq. . . .
An example of the spatial variation of train operational time for
local-only trains, over six express intervals, is illustrated in
FIGS. 14a and 14b, in which the horizontal axis is elapsed time
(rather than distance or location). Similarly, an example of the
spatial variation of train operational time for group trains over
these intervals is illustrated in FIGS. 14c and 14d. FIGS. 14a
through 14d use the average local station stop time ALST for each
interval, such an average value being constant over the intervals
by definition; FIGS. 14c and 14d use a constant extra-train delay
time value EDT for each express station, for simplicity of this
description.
[0199] As evident from a comparison of FIGS. 14c and 14d with FIGS.
14a and 14b, GEOT.sub.i>LEOT.sub.i for each interval, reflecting
that a non-zero extra-train delay time value EDT at each express
station E0 through E6. In other words, if one looks to train travel
time alone, it appears from these FIGS. 14a through 14d that the
total local train group travel time (TGOT) according to embodiments
of this invention is larger (i.e., slower) than the total local
train travel time (TLOT) under local-only service. This means that
the total passenger travel time of "LLL" passengers defined above,
who travel exclusively on local service trains for the duration of
their journey of at least one full express interval, will
necessarily be slower on subway lines that implement embodiments of
this invention. On the other hand, according to embodiments of this
invention, the passenger travel time of those passengers (EEE, EEL,
LEE, LEL) who travel at least one express interval using express
service will be less than (i.e., faster than) that of the LLL
passengers. This difference between train travel time and passenger
travel time is important in the implementation of scheduling
process 38, to ensure that the desired optimization parameter
(e.g., passenger travel time rather than train travel time) is
selected for minimization.
[0200] The above discussion uses average local station stop time
ALST, which is constant over each express interval. However, in
practice, it is contemplated that the local-only train stop time at
each express station i (i.e., time LLST.sub.i) will vary from
express station to express station, because the time that a given
train is stopped at a station in modern subway systems varies with
the number of passengers boarding and de-boarding the train at that
station. In short, the local-only train stop time LLST.sub.i at
express station E, will vary with the time of day: longer during
rush hours, and shorter during non-rush hours. Field observations
from conventional subway lines indicate that the stop time of a
local-only train at a station during rush hour can be several times
longer than the stop time of the same train during non-rush hour.
As such, proper determination of the average local station stop
time ALST considers these spatial and temporal variations:
ALST ( .tau. ) = 1 N s i = 1 N s LLST i ( .tau. ) ##EQU00001##
where .tau. is a variable corresponding to the time of day, and
N.sub.s is the total number of local stations along subway line
SLINE. In addition, it is also contemplated that the local-only
travel time LETT may also vary with the time of day, as some
extra-train delay time may occur at some local stations. The
variation of these parameters with time of day .tau. and among
express intervals i is illustrated in FIGS. 15a through 15d.
[0201] This variation of operational times with the time of day can
be approached in various ways within scheduling process 38. For
example, if the schedule is to be derived using operational times
that are fixed (for scheduling purposes) over the day, then
scheduling process 38 can be optimized by minimizing error
FSOE(.tau.) defined by:
FSOE ( .tau. ) = k = 1 K s GEOT k ( .tau. ) _ - k = 1 K s GEOT k =
TGOT ( .tau. ) _ - TGOT ##EQU00002##
where K.sub.s is the number of express stations, where the values
GEOT.sub.k(.tau.) and TGOT(.tau.) are the actual operation times
observed in practice, as varying with time over the time of day,
and where the values GEOT.sub.k and TGOT are those defined by the
fixed schedule. Another approach available within scheduling
process 38 is to vary the operational schedule dynamically over the
time of day, in that the variations with the time of day are
incorporated into the determining of the schedule in the first
place. According to that approach, scheduling process 38 can be
optimized by minimizing error DSOE(.tau.) defined by:
DSOE ( .tau. ) = k = 1 K s GEOT k ( .tau. ) _ - k = 1 K s GEOT k (
.tau. ) = TGOT ( .tau. ) _ - TGOT ( .tau. ) ##EQU00003##
where the scheduled values GEOT.sub.k(.tau.) and TGOT(.tau.) as
scheduled themselves vary with the time of day.
[0202] For example, if an average local-only stop time ALST(.tau.)
is defined as that stop time at .tau.=8:00 am, then the error value
FSOE(.tau.) evaluated at .tau.=8:00 am will be close to zero, but
the error value FSOE(.tau.) evaluated at .tau.=11:00 am will be
substantial. Conversely, if dynamic scheduling is used in
scheduling process 38 to define the schedule at .tau.=8:00 am using
the average local-only stop time ALST(.tau.=8:00 am), and to define
the schedule at .tau.=11:00 am using the average local-only stop
time ALST(.tau.=11:00 am), then the error DSOE(.tau.) will be much
lower.
[0203] Scheduling process 38 can be further refined by applying a
second dimension of temporal variation, considering the difference
in passenger load from day-to-day. In other words, differences
between normal workdays, weekends, and holidays, may be included
within the optimization process, by considering parameter such as
average local-only stop time ALST(.tau.,.kappa.) to be defined not
only with respect to time of day .tau., but also with respect to
day of the week (or month, or year, or both) .kappa.. FIGS. 16a
through 16d illustrate the travel time lines of FIGS. 14a through
14d and 15a through 15d in which the various illustrated parameters
vary spatially (i.e., with express interval i) and also temporally
with respect to time of day .tau. and calendar day .kappa..
[0204] Observations
[0205] The relative efficiencies of various approaches to the
synchronized express and local trains, according to these
embodiments of the invention, can thus be readily compared by
system 20. For example, the physical passing embodiments of this
invention utilizing side-tracks are expected to have a
substantially different passenger transfer time than that of the
virtual passing embodiments of this invention in which trains
transform between providing express and local service. Of course,
in those embodiments of the invention involving the transformation
of trains between local and express service, the passenger travel
time will be affected by the numbers of intervals that the
passenger will be traveling at local travel velocities versus
express travel velocities, the particular velocities of those
intervals (see FIG. 3d), and whether the passenger relay (or
forward transfer) option is available and utilized by the
passenger. In any event, it is believed, in connection with this
invention, that the minimization of passenger travel time will be
best accomplished by the minimization of passenger transfer times
at express stations, given that the travel velocities will tend to
be constrained. Certain general concepts have been identified by
analysis of these factors, in connection with the minimization of
passenger travel time in such train systems, as will now be
summarized for the benefit of the reader.
[0206] In a general sense, based on qualitative analysis, it is
contemplated that physical passing techniques will result in
shorter passenger travel times than achievable by virtual passing
techniques, for longer passenger journeys (in terms of the number
of express intervals). Conversely, for shorter journeys, virtual
passing techniques provide shorter passenger travel times. Of
course, as mentioned above, the infrastructure cost of virtual
passing techniques is much lower than that involved in enabling
physical passing at express stations; in addition, greater
flexibility is provided by the virtual passing techniques.
[0207] In this regard, analysis has shown, according to this
invention, that for the embodiments of the invention in which a
side track enables physical passing of local trains by express
trains, as described above relative to FIGS. 1b through 1d, 3a
through 3k, 4a through 4e, and 5a through 5k, one can minimize the
extra-train delay time EDT at express stations by selecting those
stations at which the fewest number of passengers board and
de-board express trains from outside of subway line SLINE. In other
words, if the stop time at an express station is devoted primarily
to the transfer of passengers between express and local trains,
with little time required for the boarding of new passengers and
the de-boarding of departing passengers, the express station
passenger transfer time ESPT can be minimized. Because the same
local-to-express (and vice versa) transfers will be occurring at
that express station regardless of the passenger demand of that
station, the overall passenger travel time for most passengers will
be reduced if the new and departing passengers from the express
station are minimized.
[0208] In connection with the embodiments of this invention
utilizing virtual passing at express stations, by way of
transforming trains from providing local service to providing
express service, and vice versa, analysis has shown that the
express station passenger transfer time ESPT can be minimized, and
thus the overall passenger travel time minimized, also by selecting
those stations at which the fewest number of passengers board and
de-board express trains from outside of subway line SLINE as the
express stations. In other words, use of the most lightly-used
stations as express stations will optimize passenger travel times,
for similar reasons as described above.
[0209] Also in connection with the embodiments of the invention in
which virtual passing by transforming trains from local to express,
and vice versa, overall passenger travel time can be minimized by
maximizing the use of the express mode by as many passengers as
possible, over as much of their respective trips as possible. One
way in which this can be accomplished is the use of semi-express
stations, such as described above relative to FIGS. 9a through 9c,
because passengers boarding at a semi-express station immediately
board an express train in mid-interval. However, the passenger
boarding and de-boarding time at a semi-express station does not
significantly impact the overall passenger travel time for any
passenger; those passengers boarding and de-boarding at the
semi-express station obtain the benefit of longer express travel
distances (at necessarily higher travel velocity) than they would
experience on a local train, and the stop time at the semi-express
station does not impact the express station passenger transfer time
ESPT at the full express stations. Indeed, the reason for including
a semi-express station in the first place is to avoid excessive
train wait times at the next express station. Accordingly, analysis
has shown that it is optimal to select those local stations with
the highest passenger traffic (i.e., the highest number of
passengers boarding and de-boarding) as the semi-express stations.
The time required for this large number of passengers to board and
de-board does not adversely affect the overall passenger travel
time along subway line SLINE generally.
[0210] Also in connection with the embodiments of the invention in
which virtual passing by transforming trains from local to express,
and vice versa, analysis has shown that maximization of the
passenger express mode is improved by increasing the number of
trains in a group, but at a cost of increased express station
passenger transfer time ESPT. A tradeoff therefore exists between
the benefit of adding another train to the number of trains in a
group, and this cost of increased extra-train delay time EDT. It
has been found, through this analysis that, in many real-world
cases, the use of three-train groups (two express trains for every
local train) will be optimal, as it permits the greatest number of
express passengers on the average without unduly lengthening the
express station passenger transfer time ESPT and thus the overall
passenger travel time.
[0211] Other optimization techniques and concepts will become
apparent to those skilled in the art having reference to this
specification, upon applying embodiments of this invention to
specific subway lines and systems, under real-world conditions.
[0212] Comparison of the various methods summarized in Table 2
above, and particularly the proximity with which the value in the
column "Passenger travel time saving" approaches the value in the
column "Theoretical passenger travel time saving", can thus be made
to determine the gains in efficiency obtained by the various
methods and approaches. Of particular interest are the results of
the shorter trains in the bottom-most rows of Table 2,
corresponding to the virtual passing implementations described
above in connection with FIGS. 12a through 12h. As the trains
become shorter and shorter in length, relative to the length of the
platform, the actual "Passenger travel time saving" values approach
the "Theoretical passenger travel time saving" values. It is
contemplated that these highly efficient methods can be used during
off-peak times of the day, and during off-peak days in the
week/month/year, such that subway line SLINE can be operated in a
highly efficient manner, with excellent passenger travel times, and
with a reduction in the operating cost because of the reduced
length of trains involved (and thus corresponding reductions in
fuel consumption, labor costs, and the like).
[0213] Also as evident in Table 2, the column labeled "Train group
passenger throughput" contains values that vary among the various
implementations. This value is defined, for purposes of Table 2, as
the product of the number of trains per group with the average
passenger throughput per train, and is normalized against the
local-train only service of conventional two-track subway lines
(1.0). This passenger throughput varies from a high of 6.4, for
longer train groups of four trains (three of which are express
trains) to a low of 0.25 for two-train groups with short trains
(0.10 times the length of the platform). These variations in
passenger throughput can be applied to variations in passenger
demand over each day, week, and year.
[0214] In the examples considered in connection with Table 2 and as
described above, a standard local-only headway is five minutes. To
increase the throughput on such a local-only subway line with five
minute headway by a factor of six, one must dispatch six local
trains every five minutes. which amounts to a headway of about
0.833 minutes. In contrast, operation of a four-train group
according to either of the physical or virtual passing techniques,
this same throughput gain of 6.4 can be attained with a headway of
1.25 minutes, which is dramatically safer to operate. Of course, as
mentioned above, the safety of such a system can be further
increased by use of collision avoidance systems, electromagnetic
braking, and other modern techniques.
[0215] Typically, most conventional existing local-only subway
lines commonly operate with a standard dispatching interval of five
to six minutes of headway, over the one-third of the working day
deemed to be "rush hour", at which peak passenger demand occurs. As
mentioned above, to attain the factor-of-six throughput gain during
such peak times, a local-only subway line must dispatch six times
the number of trains (assuming the shortened headway is tolerable).
In contrast, according to embodiments of this invention, this same
throughput can be attained with fewer physical trains.
[0216] In addition, this throughput increase is also useful in
off-peak times. Conventional train lines avoid unprofitable
under-loading by reducing the frequency of service during off-peak
times. Unfortunately, this has the effect of dramatically
increasing passenger wait times at the stations, which makes subway
travel less convenient and which thus often results in further
reduction in passenger demand (and, conceivably, even further
reductions in train frequency to compensate). In contrast,
according to embodiments of the invention using the shorter trains,
as summarized in the bottom-most rows of Table 2. As evident from
those entries in Table 2, a group train with two shortened trains
can effectively replace a single local-only train, while still
providing nearly 50% reduction in passenger travel time. Indeed, it
is contemplated that such short trains can be operated during most
of the day on a vast majority of the two-track subway lines
currently in use in the world, providing the advantages of reduced
operating cost and reduced passenger travel time, while maintaining
the same frequency of service as provided during peak times.
[0217] To efficiently manage these shortened train times, and
indeed variations in train length over the day/week/year according
to optimization determinations made by system 20 in light of
passenger demand, it will be useful to implement modern coupling
technologies in the trains, for example as currently in use in many
airport trains and trams. Additional safety and operational
technologies such as closed-circuit television monitoring and
automated door opening and closing can provide further improvements
in the overall flexibility and efficiency of operating a subway
line while optimizing train length relative to passenger demand, in
this manner.
[0218] It is further contemplated that modern and future
transportation technologies such as collision avoidance systems and
the like can be used to reduce train travel times, and thus
passenger travel times. For example, the implementation of
collision avoidance systems in the front and rear of each train can
enable nearly bumper-to-bumper operation of subway line SLINE, as
simultaneous or otherwise coordinated braking times can be
enforced. Additional technologies such as electromagnetic track
brakes and the like can also improve these train travel times by
reducing braking times and distances.
[0219] Dynamic Synchronized Express and Local Train Scheduling
[0220] Considering the foregoing description, in a general sense,
it is contemplated that the particular expressions and their
evaluation, for optimization of such parameters as passenger travel
time, throughput, infrastructure and rolling stock efficiency, and
the like, can be readily derived and evaluated by system 20 for a
given set of constraints or choices in the number and arrangement
of stations, trains, and other infrastructure. It is also
contemplated that statistical analysis of these parameters and
their optimization based on passenger demand generally, passenger
demand by time of day and day of the week, passenger demand by
origin and destination station, and the like, can be incorporated
into the optimization performed by system 20 in deriving, managing,
and adjusting the subway schedule. It is also contemplated that
those skilled in the art having reference to this specification
will be readily able to carry out such optimization of passenger
travel time, or optimization of other parameters important to the
subway operator or its customers, without undue
experimentation.
[0221] As mentioned above in connection with the Background of the
Invention, the passenger load during non-rush hour periods of the
workday, as well as during weekends and holidays, is much lower
than during rush hour periods. In addition, the subway system is
operating in a non-rush hour period over a large majority of the
time. According to another embodiment of this invention, separate
optimizations of the operation of one or more subway lines, for
rush hour and non-rush periods, can be performed by system 20,
according to another embodiment of this invention. According to
another aspect of this invention, the efficiency and utilization of
infrastructure, rolling stock, personnel, and other resources
during non-rush hour periods of the day can be optimized. In
addition, these embodiments of the invention, and variations
thereof, perform non-rush hour optimization and scheduling that
improves the utilization of the subway system resources during
non-rush hour operation, without significantly impacting the
frequency of service provided to the traveling public.
[0222] Referring now to FIG. 17a, in comparison with FIG. 3c, the
separate optimization and distinct operation of subway line SLINE
in non-rush hour periods relative to such operation during rush
hour will now be described. For example, the operation of express
trains EXP1, EXP2, etc. and local trains LOC0, LOC1, etc. during a
rush-hour period can correspond to that shown in FIG. 3c and
described in detail above. At each express station E1 through E6,
an express train EXPx passes a previously-arrived local train LOCy,
such passing either being performed physically (i.e., the express
train EXPx physically passes local train LOCy) or "virtually"
(i.e., the local train LOCy becomes an express train over the next
express interval, and vice versa). Considering a group train to
consist of the group of trains meeting at an express station (with
the express train physically or virtually passing the local trains
in its group), the group train dispatching interval refers to the
time interval between successive group train departure times from a
given express station. As described above, this group train
dispatching interval ("GTDI") is essentially constant over subway
line SLINE. In the example of FIG. 3c, the GTDI corresponds to the
time interval between successive points t1, t2, t3, t4, etc.
[0223] According to this embodiment of the invention, the GTDI is
scaled to be longer in non-rush hour periods than during rush hour
periods. FIG. 17a illustrates the operation of subway line SLINE in
a non-rush hour period in which the GTDI is scaled by a factor of
two. In the example of FIG. 17a, group trains depart express
station E0 at times t2, t4, t6, t8; those points thus define a GTDI
that is twice that of the rush-hour case of FIG. 3c. By doubling
the GTDI, as shown in FIG. 17a, the number of express stations is
reduced by a factor of two, because the longer GTDI results in a
longer time before an express train in one group catches the local
train in the previously-dispatched group. The express station
interval (in distance) between express stations is thus effectively
doubled, assuming a constant travel velocity for express trains
EXPx (and local trains LOCy) along the line. As such, express train
EXP1 leaving express station E0 at time t2 does not meet local
train LOC0 from the previously-dispatched group until time t4, at
express station E2 (pass point 2P10). Express train EXP2 does not
catch up to local train LOC0 from two groups prior until time t6,
at express station E3 (pass point 4P20). In the diagram of FIG.
17a, the only express stations remaining are express stations E0,
E2, E4, E6; express stations E1, E3, E5 (which operate as express
stations during rush-hour, as shown in FIG. 3c) are not operating
as express stations during this non-rush hour period.
[0224] FIG. 17b illustrates the operation of subway line SLINE in a
non-rush hour period in which the GTDI is scaled by a factor of
three from that used during rush hour (FIG. 3c). In this example,
group trains are dispatched from express station E0 at times t3,
t6, t9, etc., which triples the time interval between passing
points along line SLINE. This tripled GTDI effectively triples the
express station interval (in distance) between express stations at
which passing occurs. In this example, express train EXP1 leaving
express station E0 at time t3 does not meet local train LOC0 from
the previously-dispatched group until time t6, which occurs at
express station E3 (pass point 3P10). Similarly, express train EXP2
does not catch up to local train LOC0 from two groups prior until
time t12, at express station E6 (pass point 6P20). In this tripled
GTDI case, express stations E0, E3, E6, E9 continue to operate as
express stations, while express stations E1, E2, E4, E5, E7, E8 do
not.
[0225] According to the examples of FIGS. 17a and 17b, the scaled
or extended GTDI and express station interval operation provides
important advantages in the operation of a subway line. A foremost
advantage is that express service continues to be provided to the
subway passengers, even during non-rush hour periods, in much the
same manner as described above during rush hour periods. Many
passengers can thus take advantage of greatly reduced subway travel
time, even during these non-rush hour periods; it is contemplated
that ridership and profitability can increase over the entire day
(and year) as a result. Furthermore, it is apparent from FIGS. 17a
and 17b that the number of trains running on subway line SLINE
during non-rush hour periods is greatly reduced relative to that
during rush hour periods. This is, of course, consistent with the
much lower level of passenger demand during non-rush hour periods.
As a result, express train service can be provided in combination
with local service during these non-rush hour periods, while still
attaining a high level of train and personnel utilization. The
operational economy of the subway line during non-rush hours is
thus improved in much the same manner as during rush-hour
periods.
[0226] From the viewpoint of the subway passengers, it is of course
desirable to maintain a similar frequency of service during
non-rush hour periods as during rush hours. If the number of trains
is simply reduced by scaling the GTDI, and if those trains have the
same velocity as in the rush hour period, however, the frequency of
service will necessarily decrease. According to this embodiment of
the invention, however, good frequency of service is maintained
during non-rush hour periods, even with the scaled GTDI operation
described above, through the use of semi-express stations similarly
as described above relative to FIGS. 9b and 9c. As described above,
those semi-express stations can be served by express trains EXPx
over the express station interval, by using the time that those
express trains EXPx would otherwise be waiting at an express
station (i.e., queued behind the previously-arriving local
trains).
[0227] According to another embodiment of the invention, which will
be described in connection with FIG. 17c, additional time is
provided for express trains EXPx to make additional semi-express
stops over the first scaled express interval by advancing their
departure time from the first express station. Similarly,
additional semi-express stops can be provided over the last scaled
express interval by delaying the arrival time of express trains
EXPx at the final express. According to this embodiment of the
invention, the arrival and departure times at express stations
serving the scaled express intervals between the first and last
scaled express intervals are not altered, thus maintaining the
passing operations at intermediate express stations in the manner
described above.
[0228] FIG. 17c illustrates an example of this advanced and delayed
express train operation. In this example, the GTDI is scaled by a
factor of two from its rush-hour time, and as such the number of
express stations is reduced by a factor of two (similarly as
described above relative to FIG. 17a). However, the departures of
express trains EXPx from initial express station E0 are advanced by
a time Ta; in addition, the arrival of express trains EXPx at
terminal express station E6 are delayed by a time Td. This delay is
illustrated in FIG. 17c for the case of express train EXP2D. Rather
than departing express station E0 at time t4 (shortly before the
departure of local train LOC2), express train EXP2D departs express
station E0 at an earlier time (t4-Ta). This allows time for express
train EXP2D to make additional semi-express stops along the
interval between express stations E0 and E2, yet still catch up to
local train LOC1 at express station E1 at time t6. Express train
EXP2D travels at its usual express velocity over the interval
between express stations E2 and E4, including such semi-express
stops over that interval as allowed by the queuing time at express
station E4 as described above. Over the final express interval
between express stations E4 and E6, however, the average express
velocity of express train EXP2D is reduced by making additional
semi-express stops over that interval. As a result, the arrival
time of express strain EXP2D at express station E6 is delayed by a
time Td from time t10 (at which time non-delayed express train EXP2
would have arrived).
[0229] The number of additional semi-express stops made over the
first and last express intervals, and thus the advance departure
time Ta and the delayed arrival time Td, of course depends on the
time Tse required for making a semi-express stop. Shorter
semi-express stop times Tse will, of course, increase the number of
stops that can be made for given values Ta, Td.
[0230] Those skilled in the art having reference to this
specification will comprehend, from the example approaches
illustrated in FIGS. 17a through 17c and described above, that the
number of non-rush hour express intervals relative to the rush hour
express intervals (i.e., the scaling factor applied to the GTDI)
can vary. At an extreme, a single non-rush hour express interval
can be used, with the departure or arrival of the express train
advanced or delayed in the manner shown in FIG. 17c. A less extreme
case can use two express intervals, with an express train making a
single pass (virtual or physical) at an intermediate station; the
advanced departure and delayed arrival approach of FIG. 17c can be
used in this two interval case, if additional semi-express stops
are desired.
[0231] In any case, the scaling of the GTDI for non-rush hour time
periods, relative to that during rush hours, will necessarily
compromise the frequency of train service along the subway line,
involving a tradeoff between the economics of the subway system
(favoring greater reduction in frequency of train service) and
passenger convenience (favoring lesser reduction in frequency of
train service). The optimum value of this scaling factor and the
resulting operation is contemplated to be installation-dependent;
more specifically, the optimization of the dynamic synchronized
local and express train scheduling according to embodiments of this
invention is contemplated to depend on the length of the subway
line, the number of potential semi-express station installations,
whether the advanced departure time Td and delayed arrival time Ta
can be utilized (and if so, the values for times Td, Ta), and on
other operational methods and constraints. It is contemplated that
those skilled in the art having reference to this specification
will be readily able to optimize the implementation of these
embodiments of the invention for their specific implementations and
customer demand.
[0232] Various integer scaling factors as applied to an example of
subway line SLINE are illustrated in FIG. 17d. In this example, the
baseline rush hour implementation of subway line SLINE has twelve
express station intervals between thirteen express stations E0
through E12. For purposes of this example, four local stations (not
shown in FIG. 17d) are disposed within each express station
interval, such that the entire line SLINE includes sixty local
stations, plus the origin station E0. Also for purposes of this
example, the local train travel time along this subway line SLINE
from origin to terminus is 120 minutes, and the express train
travel time is half that, at 60 minutes. FIG. 17d illustrates the
location of express stations that result from scaling factors E=1
(i.e., no change from rush hour), E=2, E=3, E=4, and E=6.
[0233] The performance results of subway line SLINE for these
various scaling factors E are tabulated in Table 3:
TABLE-US-00003 TABLE 3 Local/express # of express Number of trains
Train # of local and one-way intervals Non-rush on track (one
Equivalent utilization express stations travel times Scaling
(non-rush hour GTDI way-local + headway efficiency (rush hour)
(minutes) factor E hour) (minutes) express) (minutes) (normalized)
60 local; Local: 120; 1 12 5 36 2.5 0.16 12 express express: 60 (24
local + (plus origin) 12 express) 2 6 10 18 5.0 0.33 (12 + 6) 3 4
15 12 7.5 0.50 (8 + 4) 4 3 20 9 10.0 0.66 (6 + 3) 6 2 30 6 15.0 1.0
(4 + 2)
The results of Table 3 are shown for the example in which the GTDI
of trains departing origin express station E0 is five minutes
(i.e., the time .DELTA.t between times t1 and t0 of FIG. 3d is five
minutes). As described above, three trains (or group trains, when
applicable) are present on every express interval: these three
trains include the express train, the local train that left
immediately after the express station at the origin end of the
express station interval, and the local train that the express
train will catch up to at the destination end of the express
station interval. As such, for the rush hour case, thirty-six
trains (twelve intervals with three trains each) are on track at
any given time along subway line SLINE. The equivalent average
train headway is 2.5 minutes in this case, since two trains are
dispatched at the origin every five minutes.
[0234] As described above, the scaling factor lengthens the express
station interval (and thus the GTDI), and thus reduces the number
of express station intervals from the rush hour value. As shown in
Table 3, scaling factor E=6 lengthens the GTDI by a factor of six,
from five minutes to thirty minutes, and reduces the number of
express intervals by a factor of six, from twelve to two. As
evident from Table 3, the higher scaling factor reduces the number
of trains on track at any given time; for scaling factor E=6,
one-sixth the number of trains are on track during non-rush hour
periods than during rush hour. Conversely, the train utilization
efficiency with scaling factor E=1 is 0.16 times (i.e., one-sixth
of) that of the non-rush hour period with scaling factor E=6.
[0235] As evident by a comparison of Table 3 for the various
scaling factors E, one can evaluate the tradeoff between subway
line economics and customer convenience. For example, considering
that operating cost is reduced by reducing the number of trains on
track, the best train utilization efficiency is that provided by
the case of the highest possible scaling factor value (which is E=6
in this example). Conversely, customer convenience is improved by
more frequency train service, or lower equivalent headway times;
this is provided by scaling factor E=1. The scaling factors E=2,
E=3, and E=4 in Table 3 and FIG. 17d thus illustrate middle ground
situations between the extreme scaling factors E=1 and E=6, any one
of which may be optimal for a particular subway line and passenger
population. It is contemplated that those skilled in the art having
reference to this specification will be readily able to evaluate
such tradeoffs, for each subway line of interest. In addition, it
is also contemplated that those skilled in the art having reference
to this specification will be able to similarly compare the
operation of the rush hour and non-rush hour alternatives relative
to a conventional subway system in which only local trains are
dispatched.
[0236] In any case, it is contemplated that the length of each of
the local and express trains utilized in the non-rush hour time
periods can be adjusted to match the relative passenger demand.
Shorter trains (or, as described above relative to FIGS. 7a through
7c, fewer trains per group) can be used during those times of day,
and days of the week or year, at which passenger demand is lower
than during rush hour. This reduction in train length will, of
course, also improve the economic performance of the subway line
throughout the day, week, and year.
[0237] The alternative implementations shown in FIGS. 17a through
17d for the non-rush hour implementation are applicable to either
physical or virtual passing occurring at express stations. However,
it is contemplated that either of these passing operations will
necessarily involve some amount of extra time at the express
station, for one or both of the trains involved. It has been
observed that this additional time, if properly considered, tends
to favor the use of semi-express stations over express stations,
because the passing time is not required for stops at semi-express
stations.
[0238] It has been discovered, through theoretical analysis of
various alternatives, that the use of two elongated express station
intervals, with a relatively large number of semi-express stations
deployed along each of the two express station intervals, can
provide optimum train utilization efficiency with acceptable
equivalent headway times. An example of this situation is shown in
FIG. 17d by the line for scaling factor E=6, in which the only
express stations are origin station E0, express station E6, and
terminus station E12 (for eastbound traffic). This is because the
number of trains on track within each express station interval
remains at three trains, for each direction; for two-way service on
a dual express station interval implementation, twelve trains total
are on track at any given time. The actual equivalent headway
experienced by passengers, relative to conventional local-only
service (as is typically implemented during non-rush hour periods),
will depend on the length of the overall subway line. For very long
subway lines (e.g., beyond a sixty-station subway line with two
hour one-way local travel time from end to end), in order to keep
the equivalent headway within acceptable bounds, the use of three
elongated express station intervals may become necessary, at a cost
of increasing the number of trains on track to nine trains in each
direction. An example of this situation is shown in FIG. 17d by the
line for scaling factor E=4, in which express stations E0, E4, E8,
and E12 are in use. In either case, semi-express stations will be
utilized by the express trains over these elongated express station
intervals.
[0239] As shown in the generalized flow diagram of FIG. 3b, and as
mentioned above, optional process 39 for generating a non-rush hour
schedule and deployment of express and subway trains can be
executed by system 20 (FIG. 3a), according to this embodiment of
the invention, considering the alternative implementations
including the various scaling factors as described above. This
non-rush hour schedule is contemplated to be in addition to the
rush hour schedule described above in connection with processes 34,
36, 38 described above. As in the case of the rush hour schedule,
the optimizations involved in generating this non-rush hour
schedule are based on various sources of data and information,
including passenger data source 33, train data source 35, and
station data sourcd 37, all of which are stored in library 32 and
which contain information such as that described above in
connection with FIG. 3b. Other data regarding other parameters
useful to the scheduling process, are accessed or otherwise
available to system 20 in carrying out the scheduling of this
non-rush hour schedule.
[0240] It is contemplated that this non-rush hour scheduling
process 39 can be carried out by way of various algorithmic
approaches, for example as executed by computational resources
within system 20 executing program instructions in an automated or
"artificial intelligence" manner. In a general sense, process 39
contemplates the execution of program instructions by computational
resources within system 20 to define the scaling factor best suited
for the particular construction of subway line, passenger demand,
and operational cost and availability of trains to subway line
SLINE. For example, these computational resources may evaluate a
cost function that expresses criteria involved in defining the
numbers, lengths, and arrangement of express intervals, trains on
track, length of the trains, and location of express and
semi-express stations to be used in these non-rush hour periods. As
described above, parameters representative of passenger throughput,
passenger travel time, passenger comfort (i.e., avoiding
overcrowded conditions), and subway train utilization, may be
reflected in the cost function that is optimized in scheduling
process 39. It is contemplated that those skilled in the art having
reference to this specification will be able to apply conventional
AI and other evaluation techniques to define the number and
frequency of express trains for the current information relative to
subway line SLINE, in this process 39.
[0241] As described above in connection with process 38,
computational resources within system 20 operate within process 39
to derive a schedule for subway line SLINE during this non-rush
hour period, in which the operation of express and local trains are
synchronized so that express and local trains meet in time only at
those stations defined as express stations. As described above,
these express stations will allow for express trains to pass the
slower-traveling local trains, either physically or virtually. This
derivation in process 39 is contemplated to be, in many cases, an
iterative process by way of which certain variables are adjusted or
incremented to identify an optimum combination given the economic,
passenger-driven, and management-specified constraints on subway
line SLINE. As described above, the schedule developed by process
39 will be communicated to passengers in process 40, and adjusted
in response to real-time operational data 41 if desired, in process
42.
IN CONCLUSION
[0242] The embodiments of this invention described in this
specification provide tremendous advantages in the construction and
operation of subway train lines, particularly in urban areas for
serving commuters and other passengers. These embodiments of this
invention enable optimization of the operation of a two-track
subway line, to provide improved passenger travel times and
improved passenger throughput without requiring massive
infrastructure costs, such as undue excavation and underground
construction in building or rebuilding subway stations, or the
construction costs of separate express rail lines. As a result, it
is contemplated that the subway overcrowding now being experienced
in many cities in the world can be reduced, at minimal additional
expense. In addition, it is contemplated that these embodiments of
the invention will provide great flexibility to the subway operator
in scheduling and operating the subway lines, and flexible and
beneficial options to many passengers in improving their travel
experience. Furthermore, it is contemplated that feedback control
and adjustment of the operation of the subway system will be
enabled by application of these optimization techniques. In
addition, embodiments of this invention enable the synchronized
connections between express and local trains to be optimized
differently in non-rush-hour periods than during rush hour periods,
which allows the system operator to fully optimize operation of
commuter rail systems at all times of the day and all days of the
week, and throughout the year.
[0243] While this invention has been described according to its
embodiments, it is of course contemplated that modifications of,
and alternatives to, these embodiments, such modifications and
alternatives obtaining the advantages and benefits of this
invention, will be apparent to those of ordinary skill in the art
having reference to this specification and its drawings. It is
contemplated that such modifications and alternatives are within
the scope of this invention as subsequently claimed herein.
* * * * *